423:
1921:" for eight of the other themes (all but 1, 5, and 12). Grothendieck wrote that the first and last themes, topological tensor products and regular configurations, were of more modest size than the others. Topological tensor products had played the role of a tool rather than of a source of inspiration for further developments; but he expected that regular configurations could not be exhausted within the lifetime of a mathematician who devoted oneself to it. He believed that the deepest themes were motives, anabelian geometry, and GaloisâTeichmĂŒller theory.
6304:
1347:
commonplace and tolerated. The letter also expressed his belief that totally unforeseen events before the end of the century would lead to an unprecedented collapse of civilization. Grothendieck added however that his views were "in no way meant as a criticism of the Royal
Academy's aims in the administration of its funds" and he added, "I regret the inconvenience that my refusal to accept the Crafoord prize may have caused you and the Royal Academy."
6314:
724:, given that he had refused to take French nationality (as that would have entailed military service against his convictions). He stayed in SĂŁo Paulo (apart from a lengthy visit in France from October 1953 - March 1954) until the end of 1954. His published work from the time spent in Brazil is still in the theory of topological vector spaces; it is there that he completed his last major work on that topic (on "metric" theory of
1317:('Harvests and Sowings', 1986), Grothendieck describes his approach to mathematics and his experiences in the mathematical community, a community that initially accepted him in an open and welcoming manner, but which he progressively perceived to be governed by competition and status. He complains about what he saw as the "burial" of his work and betrayal by his former students and colleagues after he had left the community.
1113:("long-term guest") at the IHĂS, wrote a piece about Grothendieck for a special volume published on the occasion of the IHĂS's fortieth anniversary. In that publication, Cartier notes that as the son of an antimilitary anarchist and one who grew up among the disenfranchised, Grothendieck always had a deep compassion for the poor and the downtrodden. As Cartier puts it, Grothendieck came to find
1419:, claiming that all materials published in his absence had been published without his permission. He asked that none of his work be reproduced in whole or in part and that copies of this work be removed from libraries. He characterized a website devoted to his work as "an abomination". His dictate may have been reversed in 2010.
33:
547:
and worked as a journalist. As teenagers, both of his parents had broken away from their early backgrounds. At the time of his birth, Grothendieck's mother was married to the journalist
Johannes Raddatz and initially, his birth name was recorded as "Alexander Raddatz." That marriage was dissolved in
1097:
while the city was being bombed. In 1966, he had declined to attend the
International Congress of Mathematicians (ICM) in Moscow, where he was to receive the Fields Medal. He retired from scientific life around 1970 after he had found out that IHĂS was partly funded by the military. He returned to
817:
He was so completely unknown to this group and to their professors, came from such a deprived and chaotic background, and was, compared to them, so ignorant at the start of his research career, that his fulgurating ascent to sudden stardom is all the more incredible; quite unique in the history of
1941:
Although mathematics became more and more abstract and general throughout the 20th century, it was
Alexander Grothendieck who was the greatest master of this trend. His unique skill was to eliminate all unnecessary hypotheses and burrow into an area so deeply that its inner patterns on the most
1125:
was heating up, and
Cartier suggests that this also reinforced Grothendieck's distaste at having become a mandarin of the scientific world. In addition, after several years at the IHĂS, Grothendieck seemed to cast about for new intellectual interests. By the late 1960s, he had started to become
1334:
period. The first three volumes (corresponding to Parts 0 to III of the book) were published between 1989 and 1993, while the fourth volume (Part IV) was completed and, although unpublished, copies of it as a typed manuscript are circulated. Grothendieck helped with the translation and wrote a
1346:
with an open letter to the media. He wrote that he and other established mathematicians had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community that was characterized by outright scientific theft that he believed had become
1381:
More than 20,000 pages of
Grothendieck's mathematical and other writings are held at the University of Montpellier and remain unpublished. They have been digitized for preservation and are freely available in open access through the Institut Montpelliérain Alexander Grothendieck portal.
1157:. The group published a bulletin and was dedicated to antimilitary and ecological issues. It also developed strong criticism of the indiscriminate use of science and technology. Grothendieck devoted the next three years to this group and served as the main editor of its bulletin.
766:, but the offer fell through when he refused to sign a pledge promising not to work to overthrow the United States governmentâa refusal which, he was warned, threatened to land him in prison. The prospect of prison did not worry him, so long as he could have access to books.
647:), a unique secondary school founded in 1938 by local Protestant pacifists and anti-war activists. Many of the refugee children hidden in Le Chambon attended CollĂšge CĂ©venol, and it was at this school that Grothendieck apparently first became fascinated with mathematics.
1962:
Grothendieck approached algebraic geometry by clarifying the foundations of the field, and by developing mathematical tools intended to prove a number of notable conjectures. Algebraic geometry has traditionally meant the understanding of geometric objects, such as
1390:
In 1991, Grothendieck moved to a new address that he did not share with his previous contacts in the mathematical community. Very few people visited him afterward. Local villagers helped sustain him with a more varied diet after he tried to live on a staple of
497:
and, while still producing relevant mathematical work, he withdrew from the mathematical community and devoted himself to political and religious pursuits (first
Buddhism and later, a more Catholic Christian vision). In 1991, he moved to the French village of
2360: â Weil cohomology theory for schemes over a base field, whose values are modules over the ring of Witt vectors over the base field, that replaces Zariski open sets by infinitesimal thickenings of Zariski open sets with divided power structures
1971:. In this approach, the properties of a geometric object are related to the properties of an associated ring. The space (e.g., real, complex, or projective) in which the object is defined, is extrinsic to the object, while the ring is intrinsic.
2140:
into the mainstream as an organizing principle for mathematics in general. Among its uses, category theory creates a common language for describing similar structures and techniques seen in many different mathematical systems. His notion of
1633:
with Serre. This result was his first work in algebraic geometry. Grothendieck went on to plan and execute a programme for rebuilding the foundations of algebraic geometry, which at the time were in a state of flux and under discussion in
5455:
Kleinert, Werner (2007). "Wer ist
Alexander Grothendieck? Anarchie, Mathematik, SpiritualitÀt. Eine Biographie. Teil 1: Anarchie" [Who is Alexander Grothendieck? Anarchy, mathematics, spirituality. A biography. Part 1: Anarchy.].
1168:
for two years. He then became a professor at the
University of Montpellier, where he became increasingly estranged from the mathematical community. He formally retired in 1988, a few years after having accepted a research position at the
1357:
exists. As part of the notes to this manuscript, Grothendieck described the life and the work of 18 "mutants", people whom he admired as visionaries far ahead of their time and heralding a new age. The only mathematician on his list was
2928:
1986:
is associated to every open subset of the space. Schemes have become the basic objects of study for practitioners of modern algebraic geometry. Their use as a foundation allowed geometry to absorb technical advances from other fields.
1688:
Grothendieck is noted for his mastery of abstract approaches to mathematics and his perfectionism in matters of formulation and presentation. Relatively little of his work after 1960 was published by the conventional route of the
1916:
Grothendieck wrote that, of these themes, the largest in scope was topoi, as they synthesized algebraic geometry, topology, and arithmetic. The theme that had been most extensively developed was schemes, which were the framework
1403:
located him, then carried on a brief correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". After his death, it was revealed that he lived alone in a house in
424:
1693:, circulating initially in duplicated volumes of seminar notes; his influence was to a considerable extent personal. His influence spilled over into many other branches of mathematics, for example the contemporary theory of
1533:
in studying linear maps between topological vector spaces. In a few years, he had become a leading authority on this area of functional analysisâto the extent that
Dieudonné compares his impact in this field to that of
1946:
By the 1970s, Grothendieck's work was seen as influential, not only in algebraic geometry and the allied fields of sheaf theory and homological algebra, but influenced logic, in the field of categorical logic.
854:
working groups drafting into foundational work some of the ablest French and other mathematicians of the younger generation). Grothendieck practically ceased publication of papers through the conventional,
1772:. Weil had realized that to prove such a connection, one needed a new cohomology theory, but neither he nor any other expert saw how to accomplish this until such a theory was expressed by Grothendieck.
1366:
who was claimed to have survived on the Holy Eucharist alone, Grothendieck almost starved himself to death in 1988. His growing preoccupation with spiritual matters was also evident in a letter entitled
1329:
in 2025. A partial English translation can be found on the Internet. A Japanese translation of the whole book in four volumes was completed by Tsuji Yuichi (1938â2002), a friend of Grothendieck from the
1181:
While not publishing mathematical research in conventional ways during the 1980s, he produced several influential manuscripts with limited distribution, with both mathematical and biographical content.
2100:
was intended to be the "â-adic" theory but without the choice of "â", a prime number. It did not provide the intended route to the Weil conjectures, but has been behind modern developments in
1764:
that argued for a connection between the topological characteristics of a variety and its diophantine (number theoretic) properties. For example, the number of solutions of an equation over a
1105:
While the issue of military funding was perhaps the most obvious explanation for Grothendieck's departure from the IHĂS, those who knew him say that the causes of the rupture ran more deeply.
1974:
Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study. To that end, he developed the theory of
1588:. Grothendieck took them to a higher level of abstraction and turned them into a key organising principle of his theory. He shifted attention from the study of individual varieties to his
1485:
during his time in Nancy; three children, Johanna (1959), Alexander (1961), and Mathieu (1965) with his wife Mireille Dufour; and one child with Justine Skalba, with whom he lived in a
1422:
In September 2014, almost totally deaf and blind, he asked a neighbour to buy him a revolver so he could kill himself.On 13 November 2014, aged 86, Grothendieck died in the hospital of
2002:
to their algebraic structure and now bears his name, being called "the GrothendieckâHirzebruchâRiemannâRoch theorem". The tools he developed to prove this theorem started the study of
1942:
abstract level revealed themselvesâand then, like a magician, show how the solution of old problems fell out in straightforward ways now that their real nature had been revealed.
2089:. Grothendieck's large-scale approach has been called a "visionary program". The â-adic cohomology then became a fundamental tool for number theorists, with applications to the
3007:
1160:
Although Grothendieck continued with mathematical enquiries, his standard mathematical career mostly ended when he left the IHĂS. After leaving the IHĂS, Grothendieck became a
2840:
3349:
3774:
5780:
5323:
1281:
of complex curves. Although Grothendieck never published his work in this area, the proposal inspired other mathematicians to work in the area by becoming the source of
1598:), allowing a broad generalization of many classical theorems. The first major application was the relative version of Serre's theorem showing that the cohomology of a
4337:
4272:
1697:. Although lauded as "the Einstein of mathematics", his work also provoked adverse reactions, with many mathematicians seeking out more concrete areas and problems.
996:) and providing the new more flexible and general foundations for algebraic geometry that has been adopted in the field since that time. He went on to introduce the
1991:
967:
1665:
has become established as the best universal foundation for this field, because of its expressiveness as well as its technical depth. In that setting one can use
5045:
3242:
1321:
was finally published in 2022 by Gallimard and, thanks to French science historian Alain Herreman, is also available on the Internet. An English translation by
5785:
5767:
3112:
594:, where his mother contracted the tuberculosis that would eventually cause her death in 1957. While there, Grothendieck managed to attend the local school, at
1954:, "Whole fields of mathematics speak the language that he set up. We live in this big structure that he built. We take it for grantedâthe architect is gone".
477:(IHĂS) and remained there until 1970, when, driven by personal and political convictions, he left following a dispute over military funding. He received the
5218:
1967:
and surfaces, through the study of the algebraic equations for those objects. Properties of algebraic equations are in turn studied using the techniques of
4156:
1371:
sent to 250 friends in January 1990. In it, he described his encounters with a deity and announced that a "New Age" would commence on 14 October 1996.
822:
His first works on topological vector spaces in 1953 have been successfully applied to physics and computer science, culminating in a relation between
4847:
2477:
154:
4974:
4920:
1462:(1954â62). He eventually applied for French citizenship in the early 1980s, after he was well past the age that exempted him from military service.
6383:
4255:
2977:
4036:
2149:. The emergence of a separate mathematical discipline of category theory has been attributed to Grothendieck's influence, although unintentional.
705:. The latter had recently won a Fields Medal. He showed his new student his latest paper; it ended with a list of 14 open questions, relevant for
4935:
4881:
548:
1929 and Schapiro acknowledged his paternity, but never married Hanka Grothendieck. Grothendieck had a maternal sibling, his half sister Maidi.
6363:
4832:
1353:, a 315-page manuscript written in 1987, is Grothendieck's account of how his consideration of the source of dreams led him to conclude that a
4073:
1228:
below). Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic
644:
5011:
2010:, which explores the topological properties of objects by associating them with rings. After direct contact with Grothendieck's ideas at the
1717:
988:
5485:
4955:
4901:
4204:
1274:
1170:
1645:
His foundational work on algebraic geometry is at a higher level of abstraction than all prior versions. He adapted the use of non-closed
1458:. Part of his reluctance to hold French nationality is attributed to not wishing to serve in the French military, particularly due to the
621:, although he occasionally had to seek refuge in the woods during Nazi raids, surviving at times without food or water for several days.
6348:
3287:
Peixoto, Tatiana; Bietenholza, Wolfgang (2016). "To the Memory of Alexander Grothendieck: a Great and Mysterious Genius of Mathematics".
1727:
1053:
843:
590:. He and his mother were then interned in various camps from 1940 to 1942 as "undesirable dangerous foreigners." The first camp was the
474:
237:
5812:
4125:
1737:
3000:
473:
Grothendieck began his productive and public career as a mathematician in 1949. In 1958, he was appointed a research professor at the
3207:
Luca Barbieri Viale, 'Alexander Grothendieck:entusiasmo e creativitĂ ,' in C. Bartocci, R. Betti, A. Guerraggio, R. Lucchetti (eds.,)
2849:
1824:
1618:
946:
Alexander Grothendieck's work during what is described as the "Golden Age" period at the IHĂS established several unifying themes in
3914:
3324:
2584:
1639:
1590:
979:
463:
4256:âHe was in mystic deliriumâ: was this hermit mathematician a forgotten genius whose ideas could transform AI â or a lonely madman?
3954:
506:, where he lived in seclusion, still working on mathematics and his philosophical and religious thoughts until his death in 2014.
5649:
1545:
and related fields where Grothendieck did his most important and influential work. From approximately 1955 he started to work on
971:
5582:
5107:
The Grothendieck Festschrift, Volume I: A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck
4409:
3767:
5331:
5311:
716:, from 1950 to 1953. At this time he was a leading expert in the theory of topological vector spaces. In 1953 he moved to the
5572:
5148:
5115:
4816:
4740:
4681:
4630:
4603:
4569:
4532:
4499:
4330:
3539:
2272:
2230:
2178:
dedicates one chapter to the work and life of Grothendieck, introducing his story by reference to the Japanese mathematician
5684:: This is an account of how 'Pursuing Stacks' was written in response to a correspondence in English with Ronnie Brown and
4276:
3553:
2217:(1955). "Produits Tensoriels Topologiques et Espaces Nucléaires" [Topological Tensor Products and Nuclear Spaces].
1795:, he identified twelve of his contributions that he believed qualified as "great ideas". In chronological order, they are:
4022:
2716:
1244:. The manuscript, which is being edited for publication by G. Maltsiniotis, later led to another of his monumental works,
859:
route. However, he was able to play a dominant role in mathematics for approximately a decade, gathering a strong school.
5162:
4226:
6388:
5170:
MatĂ©riaux pour l'histoire des mathĂ©matiques au XXe siĂšcle â Actes du colloque Ă la mĂ©moire de Jean DieudonnĂ© (Nice 1996)
5056:
709:. Grothendieck introduced new mathematical methods that enabled him to solve all of these problems within a few months.
5424:
5394:
5249:
5207:
3054:
2619:
5003:
4472:
4105:
3454:
5717:
4988:(1998), "La folle journĂ©e, de Grothendieck Ă Connes et Kontsevich â Ăvolution des notions d'espace et de symĂ©trie",
2447:
752:
5681:
5227:
850:
and Grothendieck. Grothendieck attracted attention by an intense and highly productive activity of seminars there (
666:
where at first he did not perform well, failing such classes as astronomy. Working on his own, he rediscovered the
5530:
1892:
1248:. Written in 1991, this latter opus of approximately 2000 pages, further developed the homotopical ideas begun in
6403:
4991:
Les relations entre les mathĂ©matiques et la physique thĂ©orique â Festschrift for the 40th anniversary of the IHĂS
2077:, of the number of points on an algebraic curve or variety of higher dimension. Grothendieck's discovery of the
670:. After three years of increasingly independent studies there, he went to continue his studies in Paris in 1948.
586:
In May 1939, Grothendieck was put on a train in Hamburg for France. Shortly afterward his father was interned in
5689:
5675:
2648:
asserts that his mother was of Jewish German descent: "what I know of his life comes from Grothendieck himself".
1290:
1130:, a physicist who joined the IHĂS faculty in 1964, said that Grothendieck came to talk to him a few times about
5959:
5805:
5081:
5041:
4999:
4985:
3476:
2645:
2194:
1106:
5685:
5004:"A mad day's work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry"
6280:
5772:
5664:
5540:
5498:
4561:
3574:
2085:
theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by his student
1929:
Grothendieck is considered by many to be the greatest mathematician of the twentieth century. In an obituary
1606:
of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point space.
1378:, published in 1990, was a three-volume collection of research papers to mark his sixtieth birthday in 1988.
772:
680:
625:
2182:. The book is a lightly fictionalized account of the world of scientific inquiry and was a finalist for the
6378:
6353:
3216:
2553:
1817:
1207:
1009:
637:
4947:
4893:
3681:
3146:, p. 2: "Beide beteiligten sich am Spanischen BĂŒrgerkrieg, nicht aktiv kĂ€mpfend, aber unterstĂŒtzend."
3115:[Scientific treasure or unreadable old paper? The mysterious archives of Alexandre Grothendieck].
6398:
3720:
3395:
2604:
2502:
2405:
2097:
2034:
theories, which use algebraic techniques to study topological objects, has influenced the development of
1855:
1622:
1562:
911:
685:, but he lacked the necessary background to follow the high-powered seminar. On the advice of Cartan and
651:
327:
2969:
1470:
Grothendieck was very close to his mother, to whom he dedicated his dissertation. She died in 1957 from
1415:
In January 2010, Grothendieck wrote the letter entitled "DĂ©claration d'intention de non-publication" to
1339:
have been translated into Spanish, as well as into a Russian translation that was published in Moscow.
266:
5949:
5386:
4698:
2599:
2589:
2569:
1799:
1514:
1442:. In 1938, aged ten, he moved to France as a refugee. Records of his nationality were destroyed in the
1269:
1195:
743:, and increasingly in algebraic geometry. It was in Lawrence that Grothendieck developed his theory of
5775:
5723:
5644:
4645:
R. P. Langlands, Modular forms and l-adic representations, Lecture Notes in Math. 349. (1973), 361â500
2952:
1029:
717:
250:
6408:
6393:
6373:
6368:
6307:
5798:
5731:
4943:
4889:
4556:
3113:"Trésor scientifique ou vieux papiers illisibles? Les mystérieuses archives d'Alexandre Grothendieck"
2868:
2624:
2523:
1934:
1138:
interested Grothendieck much more than physics, and he organized some seminars on biological topics.
1099:
663:
494:
245:
123:
5654:
5554:
5531:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 3: Spirituality"
5494:
4133:
2518:
2468:
2436:
1995:
1610:
1518:
1298:
During this period, Grothendieck also gave his consent to publishing some of his drafts for EGA on
1033:
694:
578:
as non-combatant auxiliaries. However, others state that Schapiro fought in the anarchist militia.
417:
5541:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude. Part 2: Mathematics"
4174:
2609:
2338:
2035:
823:
5280:
5260:
4524:
4386:: " mathematician of staggering accomplishment... a legendary figure in the mathematical world."
4200:
1427:
1032:
and he then conjectured the existence a further generalization of it, which is now known as the
347:
6101:
5068:
3189:
Piotr Pragacz, 'Notes on the Life and Work of Alexander Grothendieck,' in Piotr Pragacz (ed.),
2357:
2332:
1866:
1005:
629:
559:. His mother followed soon thereafter. Grothendieck was left in the care of Wilhelm Heydorn, a
5736:
5239:
4730:
4620:
4593:
4489:
4095:
4051:
3269:
3208:
2164:
in English), a novel by Puerto RicanâCosta Rican writer Carlos Fonseca is about Grothendieck.
551:
Grothendieck lived with his parents in Berlin until the end of 1933, when his father moved to
88:
6194:
5281:"Comme AppelĂ© du NĂ©ant â As If Summoned from the Void: The Life of Alexandre Grothendieck II"
3226:
3190:
3175:
2543:
2386:
2348:
2043:
1809:
1526:
1486:
919:
614:
60:
5755:
5261:"Comme AppelĂ© du NĂ©ant â As If Summoned from the Void: The Life of Alexandre Grothendieck I"
4671:
3706:
2848:
2726:
1746:
1253:
535:
roots and had been imprisoned in Russia before moving to Germany in 1922, while his mother,
180:
6358:
6343:
6338:
5700:
5617:
4579:
4159:[Alexandre Grothendieck, the greatest mathematician of the 20th century, is dead].
3549:
3526:. Lecture Notes in Mathematics. Vol. 1960. New York: Springer-Verlag. pp. 1â259.
3426:
3306:
3304:
2884:
2559:
2431:
2240:
2200:
2019:
2007:
1975:
1859:
1836:
1650:
1614:
1070:
983:
706:
603:
5465:
4756:
4372:
Alexandre Grothendieck is arguably the most important mathematician of the 20th century...
3656:
1715:
The bulk of Grothendieck's published work is collected in the monumental, yet incomplete,
1580:
Homological methods and sheaf theory had already been introduced in algebraic geometry by
1200:
1165:
8:
5640:
5178:
3921:
3845:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3826:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3807:] (in Japanese). Translated by Tsuji Yuichi (2nd ed.). Kyoto: Gendai SĆ«gaku-sha.
3805:
The Solitary Adventures of a Mathematician: A Journey into Mathematics and Self-Discovery
3652:
2594:
2579:
2463:
2426:
2317:
2183:
2146:
2121:
2109:
2074:
2070:
1877:
1831:
1678:
1666:
1603:
1550:
1546:
1498:
1241:
1161:
740:
713:
690:
486:
451:
447:
224:
216:
128:
5678:, collection of mathematical and biographical information, photos, links to his writings
5444:
4363:
3992:
3947:
3301:
2888:
2171:
2078:
1846:
1753:
1405:
997:
895:
846:(IHĂS), a new privately funded research institute that, in effect, had been created for
499:
6317:
6270:
6189:
6150:
6133:
6096:
5605:
4989:
4826:
4517:
3288:
2564:
2410:
2322:
2261:
2179:
2133:
2105:
2101:
2059:
2051:
2039:
2011:
2003:
1898:
1888:
1682:
1542:
1447:
1299:
1286:
1282:
1261:
1252:. Much of this work anticipated the subsequent development during the mid-1990s of the
1233:
947:
879:
759:
744:
736:
650:
In 1990, for risking their lives to rescue Jews, the entire village was recognized as "
536:
482:
443:
352:
220:
142:
5742:
5477:
3889:
3601:
662:
After the war, the young Grothendieck studied mathematics in France, initially at the
470:. He is considered by many to be the greatest mathematician of the twentieth century.
6313:
6231:
6199:
6145:
6118:
6064:
5998:
5876:
5568:
5548:
5535:
Third part of planned four-volume biography; crowd-financed translation into English.
5510:
5502:
5430:
5420:
5390:
5245:
5203:
5144:
5111:
4812:
4736:
4677:
4626:
4599:
4565:
4528:
4495:
4468:
4456:
4424:
4101:
3535:
3414:
2933:
2910:
2902:
2658:
2278:
2268:
2244:
2226:
2090:
1979:
1913:
writes the other terms "Ariadne's thread" and "philosophy" as effective equivalents.
1850:
1757:
1581:
1475:
1211:
1193:) is a 1600-page handwritten manuscript containing many of the ideas that led to the
1025:
1017:
806:
802:
735:
at the beginning of 1955, and there he set his old subject aside in order to work in
618:
575:
571:
6204:
5905:
5749:
5300:
5125:
3344:
1506:
847:
698:
291:
6285:
6258:
6167:
6128:
6052:
6025:
6003:
5964:
5954:
5871:
5854:
5597:
5461:
5362:
5220:
Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien
5196:
Récoltes et Semailles : réflexions et témoignage sur un passé de mathématicien
5020:
4964:
4910:
4551:
3527:
3404:
3339:
2892:
2662:
2614:
2574:
2508:
2488:
2482:
2471: â cohomology theory for algebraic varieties introduced by Grothendieck (1966)
2380:
2312:
2142:
2066:
1983:
1813:
1776:
1635:
1602:
on a complete variety is finite-dimensional; Grothendieck's theorem shows that the
1570:
1566:
1510:
1400:
1359:
1354:
1142:
1114:
1041:
1037:
1001:
963:
927:
907:
903:
883:
748:
732:
702:
667:
467:
377:
307:
286:
278:
5559:
First 4 chapters from the incomplete second part of planned four-volume biography.
5093:
5025:
2531: â in algebraic geometry, an analogue of a proper map for algebraic varieties
2267:. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers.
1306: V, published in Ulam Quarterly in 1992â1993 and later made available on the
595:
6248:
6221:
6177:
6162:
6042:
5976:
5712:
5613:
5380:
5346:
5105:
4575:
4091:
3545:
3516:
3422:
2873:"Alexander Grothendieck (1928â2014) Mathematician who rebuilt algebraic geometry"
2537:
2528:
2441:
2420:
2327:
2236:
2189:
2137:
2082:
1999:
1964:
1690:
1574:
1455:
1439:
1335:
preface for it, in which he called Tsuji his "first true collaborator". Parts of
1229:
1216:
1090:
959:
863:
856:
831:
790:
721:
532:
528:
459:
434:
337:
317:
64:
5720:
with photos from Grothendieck's life, given by Winfried Scharlau at IHES in 2009
4930:
4876:
1554:
6243:
6123:
6074:
6030:
6008:
5993:
5922:
5158:
2458:
2415:
2297:
2113:
2086:
2015:
1910:
1780:
1769:
1599:
1343:
1237:
1221:
935:
887:
875:
782:
342:
322:
312:
189:
5069:"A country of which nothing is known but the name: Grothendieck and "motives""
4230:
3531:
3192:
Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes,
2167:
The band Stone Hill All Stars have a song named after Alexander Grothendieck.
1783:
in the early 1970s after Grothendieck had largely withdrawn from mathematics.
6332:
6253:
6226:
6106:
6091:
6079:
6069:
6047:
5981:
5937:
5842:
5727:
5506:
5434:
5308:
Topics in Cohomological Studies of Algebraic Varieties: Impanga Lecture Notes
4939:
4931:
4885:
4877:
4460:
4326:
4157:"Alexandre Grothendieck, le plus grand mathématicien du XXe siÚcle, est mort"
3512:
3418:
3409:
3001:"Who is Alexander Grothendieck? Anarchy, Mathematics, Spirituality, Solitude"
2906:
2864:
2666:
2513:
2493:
2366:
1930:
1882:
1803:
1674:
1670:
1658:
1646:
1535:
1522:
1502:
1451:
1396:
1322:
1146:
1082:
1021:
1012:
to complement it. Closely linked to these cohomology theories, he originated
951:
923:
891:
810:
798:
778:
763:
591:
439:
146:
106:
5660:
5514:
5128:. "De L'analyse fonctionelle aux fondements de la géométrie algébrique". In
5046:"Un pays dont on ne connaĂźtrait que le nom (Grothendieck et les " motifs ")"
4487:
3243:"Alexandre Grothendieck, ou la mort d'un génie qui voulait se faire oublier"
3058:
1761:
1501:. Between 1949 and 1953 he worked on his doctoral thesis in this subject at
686:
6020:
5859:
5837:
5821:
5706:
5376:
4697:
Marquis, Jean-Pierre (2015). "Category Theory". In Zalta, Edward N. (ed.).
4259:
3875:
2914:
2307:
2248:
2047:
1765:
1630:
1471:
1459:
1423:
1363:
1278:
1257:
1127:
1121:" ("a gilded cage"). While Grothendieck was at the IHĂS, opposition to the
867:
725:
693:
where two leading experts were working on Grothendieck's area of interest,
674:
643:
In Le Chambon, Grothendieck attended the CollĂšge CĂ©venol (now known as the
633:
607:
599:
478:
455:
171:
84:
5893:
5405:
4781:
3745:
2391:
2282:
1454:
person for at least the majority of his working life and he traveled on a
786:
6216:
6172:
5910:
5669:
5241:
Loving and Hating Mathematics: Challenging the Myths of Mathematical Life
5085:
4994:, vol. S88, Institut des Hautes Ătudes Scientifiques, pp. 11â19
3864:] (Unpublished manuscript) (in Japanese). Translated by Tsuji Yuichi.
2548:
2343:
2117:
1968:
1443:
1416:
1122:
1086:
1078:
931:
871:
827:
587:
332:
212:
32:
2069:
were formulated in the later 1940s as a set of mathematical problems in
1047:
The results of his work on these and other topics were published in the
5927:
5888:
5609:
5097:
3994:
Die Mutanten â Les Mutants â eine Meditation von Alexander Grothendieck
3272:[Alexander Grothendieck: A journey in pursuit of the obvious].
3270:"Alexandre Grothendieck: Un voyage Ă la poursuite des choses Ă©videntes"
2955:
David Mumford at Brown and Harvard Universities: Archive for Reprints:
2777:
2775:
2670:
2055:
2031:
1951:
1585:
540:
4703:(Winter 2015 ed.). Metaphysics Research Lab, Stanford University.
3801:
Suugakusha no kodokuna bĆken : suugaku to jiko no hakken eno tabi
5672:
is a peripatetic seminar on Grothendieck view not just on mathematics
5635:
is a website devoted to the life and works of Alexandre Grothendieck.
5632:
5367:
5350:
5199:
5101:
5089:
4969:
4915:
4121:
3824:
Mathematics and the Naked King: A Dream and the Burial of Mathematics
3237:
3235:
2371:
1873:
1654:
1392:
1326:
1307:
1224:. This letter and successive parts were distributed from Bangor (see
899:
794:
524:
446:. His research extended the scope of the field and added elements of
5601:
5407:
Wer ist Alexander Grothendieck?: Anarchie, Mathematik, SpiritualitÀt
4004:
2897:
2872:
2772:
2302:
978:. Then, following the programme he outlined in his talk at the 1958
6275:
5790:
5761:
4465:
Sheaves in Geometry and Logic: a First Introduction to Topos Theory
3437:
3435:
3293:
3117:
2453:
2396:
1827:
1694:
1595:
1530:
1482:
1409:
1074:
975:
955:
598:
Once, he managed to escape from the camp, intending to assassinate
560:
503:
490:
438:; 28 March 1928 â 13 November 2014) was a German-born French
150:
3477:"1953 : un « Résumé » aux développements illimités"
3232:
712:
In Nancy, he wrote his dissertation under those two professors on
5567:, Somerville Massachusetts: International Press of Boston, Inc.,
3462:
Who Is Alexandre Grothendieck: Anarchy, Mathematics, Spirituality
1657:. As 'functions' these can take only the value 0, but they carry
1135:
1131:
610:. Grothendieck was permitted to live separated from his mother.
567:
544:
3432:
3149:
2556: â Conditions for a divisor of a local ring to be principal
1909:
denotes a kind of "meta-theory" that may be used heuristically;
657:
3195:
Springer Science & Business Media, 2006 pp-xi-xxviii p.xii.
966:. His first (pre-IHĂS) discovery in algebraic geometry was the
915:
563:
556:
520:
260:
56:
5781:
Alexandre-Grothendieck-une-mathematique-en-cathedrale-gothique
5695:
4455:
4154:
3843:
A Dream and the Burial of Mathematics: The Key to Yin and Yang
2953:
Alexander Grothendieck obituary by David Mumford and John Tate
1638:'s seminar. He outlined his programme in his talk at the 1958
401:
395:
4331:"The Rising Sea: Grothendieck on simplicity and generality I"
3213:
Springer Science & Business Media, 2007 pp.237â249 p.237.
2496: â a moduli space that exists in the category of schemes
1841:
1094:
1013:
552:
4732:
Tool and Object: A History and Philosophy of Category Theory
4037:
Les «gribouillis» d'Alexandre Grothendieck enfin sauvegardés
3210:
Vite matematiche: Protagonisti del '900, da Hilbert a Wiles,
1876:; cohomological formalism of topoi as inspiration for a new
5143:. AMS and the Société Mathématique de France. p. 600.
3524:
Foundations of Grothendieck Duality for Diagrams of Schemes
1626:
1000:
theory of schemes, providing the key tools for proving the
389:
4618:
4434:
4389:
4074:"The Mysterious Disappearance revolutionary mathematician"
2073:. They describe properties of analytic invariants, called
1779:, the last of which was settled by Grothendieck's student
1768:
reflects the topological nature of its solutions over the
1613:, which recently had been generalized to any dimension by
617:, he was sheltered and hidden in local boarding houses or
5353:
The Grothendieck I Knew: Telling, Not Hiding, Not Judging
5163:"Quelques idĂ©es maĂźtresses de l'Ćuvre de A. Grothendieck"
4488:
Dov M. Gabbay; Akihiro Kanamori; John Woods, Jr. (2012).
4097:
Unknown Quantity: A Real and Imaginary History of Algebra
3479:[1953: a "Summary" with unlimited developments].
2838:
1869:, yoga of "de Rham coefficients", "Hodge coefficients"...
1016:
theory as a generalisation of topology (relevant also in
974:
proved algebraically; in this context he also introduced
383:
5129:
5080:
4735:. Springer Science & Business Media. pp. 158â.
4625:. Springer Science & Business Media. pp. 156â.
4010:
3661:
3310:
2722:
2351: â Cartesian sections of certain fibered categories
442:
who became the leading figure in the creation of modern
4676:. Springer Science & Business Media. p. viii.
4669:
3972:
3855:
3836:
3817:
3798:
3371:
3125:
3094:
3092:
3090:
3088:
3086:
3084:
3082:
3080:
3078:
3076:
5776:
Rebellious Genius: In Memory of Alexander Grothendieck
5301:"Notes on the life and work of Alexander Grothendieck"
3820:
SĆ«gaku to hadaka no Ćsama: Aru yume to sĆ«gaku no maisĆ
3632:
3630:
3628:
3626:
3624:
3622:
3517:"Notes on derived categories and Grothendieck duality"
3034:
3032:
2817:
2815:
2813:
2811:
2809:
2807:
2794:
2792:
2790:
2706:
2704:
2702:
2700:
2698:
2696:
2694:
2692:
2690:
1629:, in 1957. It appeared in print in a paper written by
1385:
1289:. Later, it was published in two-volumes and entitled
1141:
In 1970, Grothendieck, with two other mathematicians,
267:
Produits tensoriels topologiques et espaces nucléaires
4283:
4155:
Stéphane Foucart; Philippe Pajot (14 November 2014).
3393:(1957), "Sur quelques points d'algĂšbre homologique",
2762:
2760:
2758:
2745:
2743:
2741:
2739:
2737:
2735:
769:
Comparing Grothendieck during his Nancy years to the
404:
5786:
Les-archives-insaisissables-d-alexandre-grothendieck
5768:
Les-archives-insaisissables-d-alexandre-grothendieck
5750:
Alexander Grothendieck: A Country Known Only by Name
5745:, Winfried Scharlau, Notices of the AMS 55(8), 2008.
5141:
Grothendieck-Serre Correspondence: Bilingual Edition
4713:
3325:"Topological vector spaces, by A. Grothendieck, ..."
3073:
3017:
2533:
Pages displaying wikidata descriptions as a fallback
2498:
Pages displaying wikidata descriptions as a fallback
2473:
Pages displaying wikidata descriptions as a fallback
2401:
Pages displaying wikidata descriptions as a fallback
2376:
Pages displaying wikidata descriptions as a fallback
2362:
Pages displaying wikidata descriptions as a fallback
2353:
Pages displaying wikidata descriptions as a fallback
2204:, a main character is a student of Grothendieck's.
1653:. Grothendieck also pioneered the systematic use of
1214:, Grothendieck wrote a 600-page manuscript entitled
1126:
interested in scientific areas outside mathematics.
398:
392:
386:
5053:
Réel en mathématiques-psychanalyse et mathématiques
4595:
Michael Atiyah Collected Works: Volume 7: 2002â2013
4307:
3619:
3587:
SGA1, Springer Lecture Notes 224, p. xii, xiii
3359:
3029:
2804:
2787:
2687:
2219:
Memoirs of the American Mathematical Society Series
2124:, another algebraic analogue of topological ideas.
1786:
1176:
380:
4516:
3286:
2755:
2732:
2505: â Structure for unifying cohomology theories
2374: â proposed framework for homological algebra
2260:
1752:Grothendieck's work includes the invention of the
890:. Collaborators on the SGA projects also included
5752:, Pierre Cartier, Notices of the AMS 62(4), 2015.
5638:
5237:
5139:Colmez, Pierre; Jean-Pierre, Serre, eds. (2004).
5051:, in Cartier, Pierre; Charraud, Nathalie (eds.),
4295:
3455:"Chapter 3. From student to celebrity: 1949-1952"
3441:
3155:
2841:"Alexander Grothendieck, Math Enigma, Dies at 86"
2478:List of things named after Alexander Grothendieck
2450: â On the foundations of homological algebra
2120:, are considered the background to the theory of
1098:academia a few years later as a professor at the
602:. Later, his mother Hanka was transferred to the
574:, during this time, his parents took part in the
155:List of things named after Alexander Grothendieck
6330:
5688:at Bangor, which continued until 1991. See also
5172:, SociĂ©tĂ© MathĂ©matique de France, pp. 11â19
4546:
4544:
3595:
3593:
3474:
3267:
3110:
2839:Bruce Weber; Julie Rehmeyer (14 November 2014).
1277:(CNRS). It describes new ideas for studying the
1273:("Sketch of a Programme") for a position at the
862:Officially during this time, he had as students
751:based on them, leading to the very influential "
636:to the Germans to be sent to be murdered at the
5565:Alexandre Grothendieck: A Mathematical Portrait
4619:M. Ram Murty; V. Kumar Murty (6 October 2012).
4090:
1760:theories, which explain an observation made by
1661:information, in purely algebraic settings. His
1187:La Longue Marche à travers la théorie de Galois
1020:). He also provided, by means of a categorical
466:led to revolutionary advances in many areas of
5417:Who is Alexander Grothendieck? Part 1: Anarchy
4869:
4670:Marc Levine; Fabien Morel (23 February 2007).
4622:The Mathematical Legacy of Srinivasa Ramanujan
4591:
4407:
4056:Institut Montpelliérain Alexander Grothendieck
2857:
2136:across varied mathematical structures brought
1897:"Schematic" or "arithmetic" point of view for
1584:and others, after sheaves had been defined by
1497:Grothendieck's early mathematical work was in
1051:and in less polished form in the notes of the
5806:
5411:First part of planned four-volume biography.
5012:Bulletin of the American Mathematical Society
4541:
3839:Aru yume to sĆ«gaku no maisĆ: In to yĆ no kagi
3647:
3645:
3590:
3496:
3332:Bulletin of the American Mathematical Society
2225:. Providence: American Mathematical Society.
1775:This program culminated in the proofs of the
1745:), which gathers together talks given in the
1621:was announced by Grothendieck at the initial
1609:In 1956, he applied the same thinking to the
720:in Brazil, where he immigrated by means of a
658:Studies and contact with research mathematics
5486:Notices of the American Mathematical Society
5359:Notices of the American Mathematical Society
5288:Notices of the American Mathematical Society
5268:Notices of the American Mathematical Society
5216:
5193:
5055:(in French), Editions Agalma, archived from
4956:Notices of the American Mathematical Society
4902:Notices of the American Mathematical Society
4728:
4491:Sets and Extensions in the Twentieth Century
4440:
4395:
3915:"Crafoord Prize letter, English translation"
3667:
3389:
2255:
2213:
1275:Centre National de la Recherche Scientifique
968:GrothendieckâHirzebruchâRiemannâRoch theorem
770:
678:
5709:, French originals and Spanish translations
5138:
4564:, vol. 52, New York: Springer-Verlag,
4355:
3876:"RĂ©coltes et Semailles; La Clef des Songes"
3570:The Life and Work of Alexander Grothendieck
3377:
3049:
3047:
2863:
2399: â class of special local-convex space
2046:. As part of this project, his creation of
1206:In 1983, stimulated by correspondence with
1044:, which were further developed by Verdier.
842:In 1958, Grothendieck was installed at the
5813:
5799:
5690:Alexander Grothendieck: some recollections
5238:Hersh, Reuben; John-Steiner, Vera (2011).
4948:"Alexandre Grothendieck 1928â2014, Part 2"
4894:"Alexandre Grothendieck 1928â2014, Part 1"
4831:: CS1 maint: location missing publisher (
4654:
4598:. Oxford University Press. pp. 383â.
4585:
4550:
4514:
4451:
4449:
3642:
1998:related topological properties of complex
1028:of schemes giving birth to the now famous
31:
5366:
5345:
5124:
5024:
4968:
4914:
4289:
4100:. National Academies Press. p. 314.
4067:
4065:
3492:
3490:
3408:
3343:
3292:
2896:
2444: â Local ring in commutative algebra
2050:, a category-theoretic generalization of
1559:Sur quelques points d'algĂšbre homologique
1267:In 1984, Grothendieck wrote the proposal
1077:. He strongly opposed both United States
941:
5756:Alexandre Grothendieck 1928â2014, Part 1
5726:âbiographical sketch of Grothendieck by
5528:
5475:
5454:
5442:
5414:
5403:
5321:
5278:
5258:
3990:
3978:
3945:
3907:
3679:
3203:
3201:
3170:
3168:
3166:
3164:
3143:
3131:
3098:
3044:
2821:
2798:
2710:
2585:Standard conjectures on algebraic cycles
1681:, and close analogues of the methods of
1640:International Congress of Mathematicians
1313:In the extensive autobiographical work,
980:International Congress of Mathematicians
844:Institut des hautes Ă©tudes scientifiques
531:(also known as Alexander Tanaroff), had
475:Institut des hautes Ă©tudes scientifiques
462:to its foundations, while his so-called
37:Alexander Grothendieck in Montréal, 1970
6384:German people of Russian-Jewish descent
5713:English summary of "La Clef des Songes"
5650:MacTutor History of Mathematics Archive
5562:
5538:
5298:
5176:
5157:
5040:
5032:
4998:
4984:
4848:"CORMAC MCCARTHY HAS NEVER BEEN BETTER"
4806:
4700:The Stanford Encyclopedia of Philosophy
4696:
4446:
4319:
4313:
4250:
4248:
4071:
3636:
3599:
3365:
3322:
3038:
2948:
2946:
2944:
2834:
2832:
2830:
2781:
2766:
2749:
2132:Grothendieck's emphasis on the role of
1901:and regular configurations of all kinds
514:
6331:
5478:"Who is Alexander Grothendieck ?"
5375:
5324:"Sensitivity to the Harmony of Things"
4523:. Cambridge University Press. p.
4207:from the original on 29 September 2014
4062:
3743:
3511:
3487:
3222:
3023:
2116:'s work, and Grothendieck's theory of
2025:
2014:, topological K-theory was founded by
1569:and applied their theory to show that
1220:. It began with a letter addressed to
645:Le CollÚge-Lycée Cévenol International
6364:Emigrants from Nazi Germany to France
5794:
5724:Can one explain schemes to biologists
5580:
5476:Scharlau, Winfried (September 2008).
5177:Douroux, Philippe (8 February 2012).
4946:; Coordinating Editors (April 2016).
4892:; Coordinating Editors (March 2016).
4809:When we cease to understand the world
4383:
4301:
4120:
3198:
3161:
2957:Can one explain schemes to biologists
2485: â Concept in algebraic geometry
2176:When We Cease to Understand the World
2152:
2096:Grothendieck's conjectural theory of
1978:that informally can be thought of as
1738:Fondements de la Géometrie Algébrique
1481:He had five children: a son with his
1408:, a small village at the foot of the
1149:, created a political group entitled
1064:
433:
416:
5820:
4980:from the original on 9 October 2022.
4926:from the original on 9 October 2022.
4845:
4361:
4245:
3765:
3559:from the original on 9 October 2022.
3355:from the original on 9 October 2022.
3268:Philippe Douroux (8 February 2012).
3013:from the original on 9 October 2022.
2998:
2941:
2827:
2145:is now the basic object of study in
1749:, also contains important material.
1492:
1362:. Influenced by the Catholic mystic
1295:(Cambridge University Press, 1997).
1191:The Long March Through Galois Theory
1069:Grothendieck's political views were
5317:from the original on 9 October 2022
4410:"Correspondance Grothendieck-Serre"
4343:from the original on 9 October 2022
4325:
4273:"Alexander Grothendieck - obituary"
4023:Le trésor oublié du génie des maths
3960:from the original on 9 October 2022
3890:"Free books: RĂ©coltes et semailles"
3780:from the original on 9 October 2022
3768:"Chapter 23. RĂ©coltes et Semailles"
2030:Grothendieck's construction of new
1386:Retirement into reclusion and death
1342:In 1988, Grothendieck declined the
1225:
922:there as well. Many others such as
493:. He later became professor at the
13:
6349:20th-century French mathematicians
5633:https://www.grothendieckcircle.org
3475:Guillaume Aubrun (17 March 2020).
2980:from the original on 22 March 2019
2665:and, with the Dutch mathematician
2620:Vector bundles on algebraic curves
2423: â Concept in category theory
2127:
624:His father was arrested under the
418:[ËalÉËksandÉËÉĄÊoËtnÌ©ËdiËk]
14:
6420:
5758:, Notices of the AMS 63(3), 2016.
5626:
5583:"Faisceaux algébriques cohérents"
5445:"Wer ist Alexander Grothendieck?"
3991:Scharlau, Winfried (2 May 2023),
3746:"Visiting Alexandre Grothendieck"
3180:Basic Books, 2009 pp.8ff.pp.8â15.
3177:The Artist and the Mathematician,
2657:Ruelle invented the concept of a
1872:"Topological algebra": â-stacks,
1825:GrothendieckâRiemannâRoch theorem
1728:Séminaire de géométrie algébrique
1619:GrothendieckâRiemannâRoch theorem
1594:(pairs of varieties related by a
1474:that she contracted in camps for
1450:after the war. Thus, he became a
1446:in 1945 and he did not apply for
1054:Séminaire de géométrie algébrique
986:, developing it in detail in his
673:Initially, Grothendieck attended
6312:
6303:
6302:
5682:The origins of 'Pursuing Stacks'
5217:Grothendieck, Alexander (1986).
5194:Grothendieck, Alexander (2022).
4846:Wood, Graeme (5 December 2022).
4519:Undergraduate Algebraic Geometry
4467:. Springer-Verlag New York Inc.
4362:Peck, Morgen (31 January 2007).
3856:Grothendieck, Alexander (1998).
3837:Grothendieck, Alexander (2016).
3818:Grothendieck, Alexander (2015).
3799:Grothendieck, Alexander (2015).
3499:The Artist and the Mathematician
3055:"The Early Background of Genius"
2383: â Homological construction
1791:In Grothendieck's retrospective
1787:Major mathematical contributions
1718:ĂlĂ©ments de gĂ©omĂ©trie algĂ©brique
1700:
1513:. His key contributions include
1177:Manuscripts written in the 1980s
1061:) that he directed at the IHĂS.
989:ĂlĂ©ments de gĂ©omĂ©trie algĂ©brique
777:-trained students at that time (
758:In 1957 he was invited to visit
376:
16:French mathematician (1928â2014)
4839:
4800:
4774:
4749:
4722:
4714:S. Gelfand; Yuri Manin (1988).
4707:
4690:
4663:
4648:
4639:
4612:
4592:Michael Atiyah (3 April 2014).
4515:Miles Reid (15 December 1988).
4508:
4481:
4408:Michel Raynaud (October 2003).
4401:
4377:
4265:
4219:
4193:
4167:
4148:
4114:
4084:
4044:
4030:
4016:
3984:
3939:
3882:
3868:
3858:MaisĆ (3) aruiwa yottsu no sĆsa
3849:
3830:
3811:
3792:
3759:
3737:
3713:
3699:
3673:
3581:
3563:
3505:
3468:
3447:
3383:
3345:10.1090/S0002-9904-1976-14076-1
3316:
3280:
3261:
3183:
3137:
3111:Philippe Douroux (6 May 2019).
3104:
2992:
2962:
2921:
2651:
2638:
2207:
2054:, has influenced the fields of
1185:Produced during 1980 and 1981,
972:HirzebruchâRiemannâRoch theorem
828:EinsteinâPodolskyâRosen paradox
581:
5743:Who Is Alexander Grothendieck?
5470:A review of the German edition
5322:Rehmeyer, Julie (9 May 2008),
5244:. Princeton University Press.
4716:Methods of homological algebra
3578:, vol. 113, no. 9, footnote 6.
1433:
1199:. It also includes a study of
982:, he introduced the theory of
632:, and then handed over by the
1:
5665:Mathematics Genealogy Project
5499:American Mathematical Society
5026:10.1090/S0273-0979-01-00913-2
4729:Ralph Krömer (25 June 2007).
4659:. Princeton University Press.
4562:Graduate Texts in Mathematics
4072:Galchen, Rivka (9 May 2022).
3862:Burial (3) or Four Operations
3600:Jackson, Allyn (March 1999).
3575:American Mathematical Monthly
3442:Hersh & John-Steiner 2011
3399:, Second Series (in French),
3249:(in French). 13 November 2014
3156:Hersh & John-Steiner 2011
2680:
1649:, which led to the theory of
1565:in 1957) where he introduced
1553:, producing the influential "
1024:, an algebraic definition of
837:
626:Vichy anti-Jewish legislation
145:and synthesis between it and
5563:Schneps, Leila, ed. (2014),
5306:, in Pragracz, Piotr (ed.),
5198:(in French). Paris, France:
4364:"Equality of Mathematicians"
2335: â Mathematical concept
1924:
1889:anabelian algebraic geometry
1808:"Continuous" and "discrete"
1685:, all in an integrated way.
1083:Soviet military expansionism
1010:algebraic de Rham cohomology
638:Auschwitz concentration camp
537:Johanna "Hanka" Grothendieck
7:
5581:Serre, Jean-Pierre (1955).
5529:Scharlau, Winfried (2010).
5450:(in German). pp. 1â22.
5443:Scharlau, Winfried (n.d.).
5415:Scharlau, Winfried (2011).
5404:Scharlau, Winfried (2007),
5226:(in French). Archived from
4870:Sources and further reading
3396:Tohoku Mathematical Journal
3323:HorvĂąth, John (July 1976).
2669:, produced a new model for
2605:Theorem on formal functions
2503:Motive (algebraic geometry)
2448:Grothendieck's TĂŽhoku paper
2290:
1957:
1950:According to mathematician
1862:(Grothendieck â-categories)
1800:Topological tensor products
1623:Mathematische Arbeitstagung
1563:Tohoku Mathematical Journal
1515:topological tensor products
1369:Lettre de la Bonne Nouvelle
1153:âthe name later changed to
1093:in the forests surrounding
1040:theory, he also introduced
652:Righteous Among the Nations
529:Alexander "Sascha" Schapiro
238:Institut des hautes Ă©tudes
10:
6425:
5387:Princeton University Press
5361:(August 2019): 1069â1077.
4807:Labatut, BenjamĂn (2020).
3707:"Publication Announcement"
2600:Theorem of absolute purity
2570:Semistable abelian variety
1573:may be defined as certain
970:, a generalisation of the
6298:
5828:
5382:The Mathematician's Brain
5126:Dieudonné, Jean Alexandre
4494:. Elsevier. p. 733.
4423:(9): 1086. Archived from
3946:Grothendieck, Alexander.
3680:Grothendieck, Alexandre.
3532:10.1007/978-3-540-85420-3
2540: â Seminal math text
2524:Projective tensor product
2263:Topological Vector Spaces
2081:, the first example of a
1893:GaloisâTeichmĂŒller theory
1529:, and the application of
1519:topological vector spaces
1465:
1438:Grothendieck was born in
1100:University of Montpellier
1085:. To protest against the
1036:. As a framework for his
771:
747:and the reformulation of
695:topological vector spaces
679:
664:University of Montpellier
519:Grothendieck was born in
495:University of Montpellier
361:
300:
277:
259:
246:University of Montpellier
230:
208:
201:
160:
137:
124:University of Montpellier
116:
96:
71:
42:
30:
23:
5655:University of St Andrews
5645:"Alexander Grothendieck"
5279:Jackson, Allyn (2004b),
5259:Jackson, Allyn (2004a),
5179:"Alexandre Grothendieck"
4782:"Alexander Grothendieck"
3651:Alexandre Grothendieck,
3481:Images des Mathématiques
3274:Images des mathématiques
2631:
2554:RamanujamâSamuel theorem
2519:Parafactorial local ring
2469:Infinitesimal cohomology
2437:Fundamental group scheme
1376:Grothendieck Festschrift
1292:Geometric Galois Actions
1111:visiteur de longue durée
1034:fundamental group scheme
866:(who worked on SGA3, on
773:Ăcole Normale SupĂ©rieure
681:Ăcole Normale SupĂ©rieure
481:in 1966 for advances in
6389:Nancy-Université alumni
5701:"RĂ©coltes et Semailles"
5539:Schneps, Leila (n.d.).
5299:Pragacz, Piotr (2005),
5031:English translation of
4179:Secret Blogging Seminar
4175:"Grothendieck's letter"
4126:"The Einstein of maths"
3682:"RĂ©coltes et Semailles"
3653:Esquisse d'un Programme
3391:Grothendieck, Alexander
3378:Colmez & Serre 2004
2610:Ultrabornological space
2406:DunfordâPettis property
2257:Grothendieck, Alexander
2215:Grothendieck, Alexander
2106:motivic homotopy theory
2079:â-adic Ă©tale cohomology
2036:algebraic number theory
1270:Esquisse d'un Programme
1254:motivic homotopy theory
1196:Esquisse d'un programme
1079:intervention in Vietnam
1030:Ă©tale fundamental group
824:Grothendieck inequality
718:University of SĂŁo Paulo
634:French Vichy government
509:
251:University of SĂŁo Paulo
6404:Scientists from Berlin
5670:SĂ©minaire Grothendieck
5661:Alexander Grothendieck
3721:"Harvests and Sowings"
3497:Amir D. Aczel (2009).
3410:10.2748/tmj/1178244839
2625:Zariski's main theorem
2358:Crystalline cohomology
2333:Approximation property
1944:
1867:crystalline cohomology
1591:relative point of view
1527:Schwartz distributions
1089:, he gave lectures on
1006:crystalline cohomology
820:
731:Grothendieck moved to
630:Drancy internment camp
464:"relative" perspective
372:Alexandre Grothendieck
368:Alexander Grothendieck
109:(post 1945 until 1971)
25:Alexander Grothendieck
5737:Archives Grothendieck
5703:, Spanish translation
5696:RĂ©coltes et Semailles
5590:Annals of Mathematics
5130:Cartier et al. (2007)
5066:English translation:
4201:"Grothendieck Circle"
2784:, p. 10, footnote 12.
2544:Quasi-finite morphism
2387:Descent (mathematics)
2349:Crystal (mathematics)
2044:representation theory
1939:
1793:RĂ©coltes et Semailles
1337:RĂ©coltes et Semailles
1325:will be published by
1319:RĂ©coltes et Semailles
1315:RĂ©coltes et Semailles
1300:Bertini-type theorems
920:nonabelian cohomology
918:theory extensions of
874:(cotangent complex),
815:
707:locally convex spaces
615:Le Chambon-sur-Lignon
606:for the remainder of
527:parents. His father,
5707:"La Clef des Songes"
5641:Robertson, Edmund F.
5553:: CS1 maint: year (
4279:on 15 November 2014.
3948:"La Clef des Songes"
3766:Scharlau, Winfried.
2999:Scharlau, Winfried.
2970:"Fields Medals 1966"
2560:Scheme (mathematics)
2432:Fundamental groupoid
2134:universal properties
2075:local zeta functions
2020:Friedrich Hirzebruch
2008:topological K-theory
1996:RiemannâRoch theorem
1860:motivic Galois group
1611:RiemannâRoch theorem
1604:higher direct images
1525:as foundational for
1489:in the early 1970s.
1444:fall of Nazi Germany
1428:Saint-Girons, AriĂšge
1236:and prospects for a
938:were also involved.
604:Gurs internment camp
515:Family and childhood
6379:Functional analysts
6354:Algebraic geometers
5676:Grothendieck Circle
5639:O'Connor, John J.;
5419:. Books on Demand.
5355:By Paulo Ribenboim"
5334:on 16 February 2012
4673:Algebraic Cobordism
4655:J.S. Milne (1980).
4227:"RĂ©Ă©dition des SGA"
4054:[Welcome].
4011:Cartier et al. 2007
3657:English translation
3602:"The IHĂS at Forty"
3311:Cartier et al. 2007
3247:Libération Sciences
2929:"Guardian obituary"
2889:2015Natur.517..272M
2723:Cartier et al. 2007
2595:Tannakian formalism
2590:Sketch of a program
2580:Stack (mathematics)
2464:Homotopy hypothesis
2427:Formally smooth map
2339:BarsottiâTate group
2318:Accessible category
2184:National Book Award
2147:homological algebra
2122:algebraic cobordism
2110:motivic integration
2071:arithmetic geometry
2026:Cohomology theories
1878:homotopical algebra
1832:intersection theory
1679:commutative algebra
1667:birational geometry
1561:, published in the
1551:homological algebra
1541:It is, however, in
1499:functional analysis
1310:web site in 2004).
1308:Grothendieck Circle
1162:temporary professor
882:(co-founder of the
741:homological algebra
714:functional analysis
691:University of Nancy
487:homological algebra
452:homological algebra
448:commutative algebra
435:[ÉĄÊÉtÉndik]
225:homological algebra
217:functional analysis
129:University of Nancy
6399:Operator theorists
6318:Mathematics portal
5718:Video of a lecture
5233:on 18 August 2017.
4757:"Colonel LĂĄgrimas"
4557:Algebraic Geometry
4430:on 3 October 2003.
4417:Notices of the AMS
3709:. 25 January 2023.
3609:Notices of the AMS
3483:(in French). CNRS.
3276:(in French). CNRS.
2959:, 14 December 2014
2853:on 1 January 2022.
2845:The New York Times
2565:Section conjecture
2411:Effaceable functor
2323:Algebraic geometry
2180:Shinichi Mochizuki
2153:In popular culture
2102:algebraic K-theory
2060:mathematical logic
2052:point-set topology
2040:algebraic topology
2012:Bonn Arbeitstagung
1980:topological spaces
1814:derived categories
1747:SĂ©minaire Bourbaki
1735:). The collection
1683:algebraic topology
1669:, techniques from
1567:abelian categories
1543:algebraic geometry
1448:French citizenship
1351:La Clef des Songes
1287:anabelian geometry
1262:Vladimir Voevodsky
1234:algebraic geometry
1210:and Tim Porter at
1201:TeichmĂŒller theory
1065:Political activism
1042:derived categories
1026:fundamental groups
948:algebraic geometry
880:Jean-Louis Verdier
760:Harvard University
745:abelian categories
737:algebraic topology
689:, he moved to the
628:, and sent to the
613:In the village of
483:algebraic geometry
444:algebraic geometry
353:Jean-Louis Verdier
221:algebraic geometry
181:Ămile Picard Medal
143:algebraic geometry
6326:
6325:
5574:978-1-57146-282-4
5150:978-1-4704-6939-9
5117:978-0-8176-4566-3
5102:Ribet, Kenneth A.
5090:Katz, Nicholas M.
4818:978-1-68137-566-3
4742:978-3-7643-7524-9
4683:978-3-540-36824-3
4632:978-81-322-0769-6
4605:978-0-19-968926-2
4571:978-0-387-90244-9
4552:Hartshorne, Robin
4534:978-0-521-35662-6
4501:978-0-444-51621-3
4457:Saunders Mac Lane
4441:Grothendieck 1986
4396:Grothendieck 1986
4181:. 9 February 2010
4136:on 11 August 2016
4124:(20 March 2004).
3927:on 6 January 2006
3668:Grothendieck 2022
3541:978-3-540-85419-7
2934:Independent.co.uk
2673:during the 1970s.
2659:strange attractor
2274:978-0-677-30020-7
2232:978-0-8218-1216-7
2091:Langlands program
1994:of the classical
1899:regular polyhedra
1851:l-adic cohomology
1758:l-adic cohomology
1663:theory of schemes
1582:Jean-Pierre Serre
1577:in this context.
1493:Mathematical work
1476:displaced persons
1395:. At some point,
1212:Bangor University
1166:CollĂšge de France
1155:Survivre et vivre
1018:categorical logic
908:Lefschetz pencils
807:Bernard Malgrange
803:Jean-Pierre Serre
576:Spanish Civil War
572:Winfried Scharlau
543:German family in
365:
364:
301:Doctoral students
279:Doctoral advisors
203:Scientific career
103:French since 1971
6416:
6409:Stateless people
6394:Nicolas Bourbaki
6374:French pacifists
6369:Fields Medalists
6316:
6306:
6305:
5822:Fields Medalists
5815:
5808:
5801:
5792:
5791:
5773:Kutateladze S.S.
5764:by Mateo Carmona
5657:
5621:
5587:
5577:
5558:
5552:
5544:
5534:
5525:
5523:
5521:
5482:
5469:
5451:
5449:
5439:English version.
5438:
5410:
5400:
5372:
5370:
5368:10.1090/noti1909
5347:Ribenboim, Paulo
5342:
5341:
5339:
5330:, archived from
5318:
5316:
5305:
5295:
5285:
5275:
5265:
5255:
5234:
5232:
5225:
5213:
5190:
5188:
5186:
5173:
5167:
5154:
5133:
5121:
5104:, eds. (2007) .
5075:
5073:
5063:
5061:
5050:
5030:
5028:
5008:
4995:
4981:
4979:
4972:
4970:10.1090/noti1361
4952:
4927:
4925:
4918:
4916:10.1090/noti1336
4898:
4863:
4862:
4860:
4858:
4843:
4837:
4836:
4830:
4822:
4811:. New York, NY.
4804:
4798:
4797:
4795:
4793:
4788:. 23 August 2017
4778:
4772:
4771:
4769:
4767:
4753:
4747:
4746:
4726:
4720:
4719:
4711:
4705:
4704:
4694:
4688:
4687:
4667:
4661:
4660:
4657:Ătale cohomology
4652:
4646:
4643:
4637:
4636:
4616:
4610:
4609:
4589:
4583:
4582:
4548:
4539:
4538:
4522:
4512:
4506:
4505:
4485:
4479:
4478:
4453:
4444:
4438:
4432:
4431:
4429:
4414:
4405:
4399:
4393:
4387:
4381:
4375:
4374:
4359:
4353:
4352:
4350:
4348:
4342:
4335:
4323:
4317:
4311:
4305:
4299:
4293:
4287:
4281:
4280:
4275:. Archived from
4269:
4263:
4252:
4243:
4242:
4240:
4238:
4229:. Archived from
4223:
4217:
4216:
4214:
4212:
4197:
4191:
4190:
4188:
4186:
4171:
4165:
4164:
4152:
4146:
4145:
4143:
4141:
4132:. Archived from
4118:
4112:
4111:
4088:
4082:
4081:
4069:
4060:
4059:
4048:
4042:
4041:
4034:
4028:
4027:
4020:
4014:
4008:
4002:
4001:
3999:
3988:
3982:
3976:
3970:
3969:
3967:
3965:
3959:
3952:
3943:
3937:
3936:
3934:
3932:
3926:
3920:. Archived from
3919:
3911:
3905:
3904:
3902:
3900:
3886:
3880:
3879:
3872:
3866:
3865:
3853:
3847:
3846:
3834:
3828:
3827:
3815:
3809:
3808:
3796:
3790:
3789:
3787:
3785:
3779:
3772:
3763:
3757:
3756:
3754:
3752:
3741:
3735:
3734:
3732:
3730:
3725:
3717:
3711:
3710:
3703:
3697:
3696:
3694:
3692:
3686:
3677:
3671:
3665:
3659:
3649:
3640:
3634:
3617:
3616:
3606:
3597:
3588:
3585:
3579:
3567:
3561:
3560:
3558:
3521:
3509:
3503:
3502:
3494:
3485:
3484:
3472:
3466:
3465:
3459:
3451:
3445:
3439:
3430:
3429:
3412:
3387:
3381:
3375:
3369:
3363:
3357:
3356:
3354:
3347:
3330:. Book Reviews.
3329:
3320:
3314:
3308:
3299:
3298:
3296:
3284:
3278:
3277:
3265:
3259:
3258:
3256:
3254:
3239:
3230:
3220:
3214:
3205:
3196:
3187:
3181:
3172:
3159:
3153:
3147:
3141:
3135:
3129:
3123:
3122:
3108:
3102:
3096:
3071:
3070:
3068:
3066:
3057:. Archived from
3051:
3042:
3036:
3027:
3021:
3015:
3014:
3012:
3005:
2996:
2990:
2989:
2987:
2985:
2966:
2960:
2950:
2939:
2938:
2925:
2919:
2918:
2900:
2861:
2855:
2854:
2852:
2847:. Archived from
2836:
2825:
2819:
2802:
2796:
2785:
2779:
2770:
2764:
2753:
2747:
2730:
2720:
2714:
2708:
2674:
2663:dynamical system
2655:
2649:
2642:
2615:Weil conjectures
2575:Sheaf cohomology
2534:
2509:Nuclear operator
2499:
2489:Nakai conjecture
2483:Local cohomology
2474:
2402:
2381:Derived category
2377:
2363:
2354:
2313:Abelian category
2286:
2266:
2252:
2172:BenjamĂn Labatut
2158:Colonel LĂĄgrimas
2143:abelian category
2067:Weil conjectures
2000:algebraic curves
1984:commutative ring
1965:algebraic curves
1847:Ătale cohomology
1777:Weil conjectures
1636:Claude Chevalley
1575:derived functors
1571:sheaf cohomology
1521:, the theory of
1511:Laurent Schwartz
1505:, supervised by
1406:Lasserre, AriĂšge
1360:Bernhard Riemann
1143:Claude Chevalley
1115:Bures-sur-Yvette
1038:coherent duality
1002:Weil conjectures
998:Ă©tale cohomology
964:complex analysis
928:Robin Hartshorne
904:monodromy theory
896:Ă©tale cohomology
884:derived category
776:
775:
749:sheaf cohomology
733:Lawrence, Kansas
703:Laurent Schwartz
684:
683:
668:Lebesgue measure
468:pure mathematics
437:
432:
428:
427:
426:
420:
415:
411:
410:
407:
406:
403:
400:
397:
394:
391:
388:
385:
382:
308:Pierre Berthelot
287:Laurent Schwartz
273:
194:
187:
178:
169:
81:
79:
76:13 November 2014
52:
50:
35:
21:
20:
6424:
6423:
6419:
6418:
6417:
6415:
6414:
6413:
6329:
6328:
6327:
6322:
6294:
6293:
6290:
6263:
6236:
6209:
6182:
6155:
6138:
6111:
6084:
6057:
6035:
6013:
5986:
5969:
5942:
5915:
5898:
5881:
5864:
5847:
5824:
5819:
5762:A. Grothendieck
5629:
5624:
5602:10.2307/1969915
5585:
5575:
5546:
5545:
5519:
5517:
5480:
5447:
5427:
5397:
5337:
5335:
5314:
5303:
5294:(10): 1196â1212
5283:
5263:
5252:
5230:
5223:
5210:
5184:
5182:
5165:
5159:Deligne, Pierre
5151:
5118:
5082:Cartier, Pierre
5071:
5067:
5062:on 4 March 2016
5059:
5048:
5042:Cartier, Pierre
5006:
5000:Cartier, Pierre
4986:Cartier, Pierre
4977:
4963:(4): 401â2413.
4950:
4923:
4896:
4872:
4867:
4866:
4856:
4854:
4844:
4840:
4824:
4823:
4819:
4805:
4801:
4791:
4789:
4780:
4779:
4775:
4765:
4763:
4755:
4754:
4750:
4743:
4727:
4723:
4712:
4708:
4695:
4691:
4684:
4668:
4664:
4653:
4649:
4644:
4640:
4633:
4617:
4613:
4606:
4590:
4586:
4572:
4549:
4542:
4535:
4513:
4509:
4502:
4486:
4482:
4475:
4454:
4447:
4439:
4435:
4427:
4415:. Book Review.
4412:
4406:
4402:
4394:
4390:
4382:
4378:
4360:
4356:
4346:
4344:
4340:
4333:
4324:
4320:
4312:
4308:
4300:
4296:
4288:
4284:
4271:
4270:
4266:
4253:
4246:
4236:
4234:
4233:on 29 June 2016
4225:
4224:
4220:
4210:
4208:
4199:
4198:
4194:
4184:
4182:
4173:
4172:
4168:
4153:
4149:
4139:
4137:
4119:
4115:
4108:
4092:John Derbyshire
4089:
4085:
4070:
4063:
4050:
4049:
4045:
4039:
4035:
4031:
4025:
4021:
4017:
4009:
4005:
3997:
3989:
3985:
3977:
3973:
3963:
3961:
3957:
3950:
3944:
3940:
3930:
3928:
3924:
3917:
3913:
3912:
3908:
3898:
3896:
3888:
3887:
3883:
3874:
3873:
3869:
3854:
3850:
3835:
3831:
3816:
3812:
3797:
3793:
3783:
3781:
3777:
3770:
3764:
3760:
3750:
3748:
3742:
3738:
3728:
3726:
3723:
3719:
3718:
3714:
3705:
3704:
3700:
3690:
3688:
3684:
3678:
3674:
3666:
3662:
3650:
3643:
3635:
3620:
3604:
3598:
3591:
3586:
3582:
3568:
3564:
3556:
3542:
3519:
3510:
3506:
3495:
3488:
3473:
3469:
3457:
3453:
3452:
3448:
3440:
3433:
3388:
3384:
3376:
3372:
3364:
3360:
3352:
3327:
3321:
3317:
3309:
3302:
3285:
3281:
3266:
3262:
3252:
3250:
3241:
3240:
3233:
3221:
3217:
3206:
3199:
3188:
3184:
3173:
3162:
3154:
3150:
3142:
3138:
3130:
3126:
3109:
3105:
3097:
3074:
3064:
3062:
3061:on 15 June 2011
3053:
3052:
3045:
3037:
3030:
3022:
3018:
3010:
3003:
2997:
2993:
2983:
2981:
2968:
2967:
2963:
2951:
2942:
2927:
2926:
2922:
2898:10.1038/517272a
2862:
2858:
2837:
2828:
2820:
2805:
2797:
2788:
2780:
2773:
2765:
2756:
2748:
2733:
2721:
2717:
2709:
2688:
2683:
2678:
2677:
2656:
2652:
2643:
2639:
2634:
2629:
2538:Pursuing Stacks
2532:
2529:Proper morphism
2497:
2472:
2442:Gorenstein ring
2421:Fibred category
2400:
2375:
2361:
2352:
2328:Algebraic stack
2293:
2275:
2233:
2210:
2198:and its sequel
2190:Cormac McCarthy
2155:
2138:category theory
2130:
2128:Category theory
2112:. This theory,
2083:Weil cohomology
2028:
1960:
1927:
1789:
1770:complex numbers
1713:
1691:learned journal
1495:
1468:
1456:Nansen passport
1436:
1388:
1283:dessin d'enfant
1250:Pursuing Stacks
1246:Les DĂ©rivateurs
1230:homotopy theory
1217:Pursuing Stacks
1179:
1091:category theory
1067:
960:category theory
944:
864:Michel Demazure
857:learned journal
840:
832:quantum physics
791:Jacques Dixmier
722:Nansen passport
660:
584:
570:. According to
566:and teacher in
517:
512:
460:category theory
430:
422:
421:
413:
379:
375:
357:
348:HoĂ ng XuĂąn SĂnh
338:William Messing
318:Michel Demazure
296:
271:
255:
239:
197:
192:
185:
176:
167:
153:
133:
117:Alma mater
112:
92:
82:
77:
75:
67:
54:
48:
46:
38:
26:
17:
12:
11:
5:
6422:
6412:
6411:
6406:
6401:
6396:
6391:
6386:
6381:
6376:
6371:
6366:
6361:
6356:
6351:
6346:
6341:
6324:
6323:
6321:
6320:
6310:
6299:
6296:
6295:
6292:
6291:
6289:
6288:
6283:
6278:
6273:
6266:
6264:
6262:
6261:
6256:
6251:
6246:
6239:
6237:
6235:
6234:
6229:
6224:
6219:
6212:
6210:
6208:
6207:
6202:
6197:
6192:
6185:
6183:
6181:
6180:
6175:
6170:
6165:
6158:
6156:
6154:
6153:
6148:
6141:
6139:
6137:
6136:
6131:
6126:
6121:
6114:
6112:
6110:
6109:
6104:
6099:
6094:
6087:
6085:
6083:
6082:
6077:
6072:
6067:
6060:
6058:
6056:
6055:
6050:
6045:
6038:
6036:
6034:
6033:
6028:
6023:
6016:
6014:
6012:
6011:
6006:
6001:
5996:
5989:
5987:
5985:
5984:
5979:
5972:
5970:
5968:
5967:
5962:
5957:
5952:
5945:
5943:
5941:
5940:
5935:
5930:
5925:
5918:
5916:
5914:
5913:
5908:
5901:
5899:
5897:
5896:
5891:
5884:
5882:
5880:
5879:
5874:
5867:
5865:
5863:
5862:
5857:
5850:
5848:
5846:
5845:
5840:
5833:
5830:
5829:
5826:
5825:
5818:
5817:
5810:
5803:
5795:
5789:
5788:
5783:
5778:
5770:
5765:
5759:
5753:
5746:
5739:
5734:
5721:
5715:
5710:
5704:
5698:
5693:
5679:
5673:
5667:
5658:
5636:
5628:
5627:External links
5625:
5623:
5622:
5596:(2): 197â278.
5578:
5573:
5560:
5536:
5526:
5495:Providence, RI
5473:
5472:
5471:
5452:
5440:
5426:978-3842340923
5425:
5401:
5396:978-0691129822
5395:
5373:
5351:"Excerpt from
5343:
5319:
5310:, BirkhÀuser,
5296:
5276:
5274:(4): 1038â1056
5256:
5251:978-1400836116
5250:
5235:
5214:
5209:978-2073004833
5208:
5191:
5174:
5155:
5149:
5136:
5135:
5134:
5116:
5110:. BirkhÀuser.
5098:Manin, Yuri I.
5094:Laumon, GĂ©rard
5078:
5077:
5076:
5038:
5037:
5036:
5033:Cartier (1998)
5019:(4): 389â408.
4982:
4928:
4909:(3): 242â255.
4873:
4871:
4868:
4865:
4864:
4838:
4817:
4799:
4773:
4761:Restless Books
4748:
4741:
4721:
4706:
4689:
4682:
4662:
4647:
4638:
4631:
4611:
4604:
4584:
4570:
4540:
4533:
4507:
4500:
4480:
4473:
4445:
4433:
4400:
4388:
4376:
4354:
4327:McLarty, Colin
4318:
4306:
4294:
4290:Dieudonné 2007
4282:
4264:
4262:31 August 2024
4244:
4218:
4192:
4166:
4147:
4113:
4106:
4083:
4078:The New Yorker
4061:
4043:
4029:
4015:
4003:
3983:
3981:, p. 940.
3971:
3938:
3906:
3881:
3867:
3848:
3829:
3810:
3791:
3758:
3736:
3712:
3698:
3672:
3660:
3641:
3618:
3589:
3580:
3562:
3540:
3513:Lipman, Joseph
3504:
3501:. Basic Books.
3486:
3467:
3464:. Vol. 2.
3446:
3444:, p. 113.
3431:
3403:(2): 119â221,
3382:
3370:
3358:
3338:(4): 515â521.
3315:
3300:
3279:
3260:
3231:
3215:
3197:
3182:
3174:Amir D. Aczel,
3160:
3158:, p. 109.
3148:
3136:
3134:, p. 931.
3124:
3103:
3072:
3043:
3028:
3016:
2991:
2961:
2940:
2920:
2865:Mumford, David
2856:
2826:
2803:
2786:
2771:
2754:
2731:
2715:
2685:
2684:
2682:
2679:
2676:
2675:
2650:
2646:Pierre Cartier
2636:
2635:
2633:
2630:
2628:
2627:
2622:
2617:
2612:
2607:
2602:
2597:
2592:
2587:
2582:
2577:
2572:
2567:
2562:
2557:
2551:
2546:
2541:
2535:
2526:
2521:
2516:
2511:
2506:
2500:
2491:
2486:
2480:
2475:
2466:
2461:
2459:Hilbert scheme
2456:
2451:
2445:
2439:
2434:
2429:
2424:
2418:
2416:Excellent ring
2413:
2408:
2403:
2394:
2389:
2384:
2378:
2369:
2364:
2355:
2346:
2341:
2336:
2330:
2325:
2320:
2315:
2310:
2305:
2300:
2294:
2292:
2289:
2288:
2287:
2273:
2253:
2231:
2209:
2206:
2154:
2151:
2129:
2126:
2114:Daniel Quillen
2087:Pierre Deligne
2027:
2024:
2016:Michael Atiyah
1992:generalization
1959:
1956:
1926:
1923:
1919:par excellence
1911:Michel Raynaud
1905:Here the term
1903:
1902:
1895:
1885:
1880:
1870:
1863:
1853:
1844:
1839:
1834:
1830:relation with
1821:
1818:six operations
1806:
1804:nuclear spaces
1788:
1785:
1781:Pierre Deligne
1712:
1699:
1647:generic points
1600:coherent sheaf
1523:nuclear spaces
1507:Jean Dieudonné
1494:
1491:
1467:
1464:
1440:Weimar Germany
1435:
1432:
1393:dandelion soup
1387:
1384:
1344:Crafoord Prize
1238:noncommutative
1226:External links
1222:Daniel Quillen
1178:
1175:
1119:une cage dorée
1107:Pierre Cartier
1066:
1063:
943:
940:
936:C.P. Ramanujam
888:Pierre Deligne
876:Michel Raynaud
848:Jean Dieudonné
839:
836:
783:Roger Godement
699:Jean Dieudonné
677:'s Seminar at
659:
656:
583:
580:
539:, came from a
533:Hasidic Jewish
516:
513:
511:
508:
363:
362:
359:
358:
356:
355:
350:
345:
343:Michel Raynaud
340:
335:
330:
325:
323:Pierre Gabriel
320:
315:
313:Pierre Deligne
310:
304:
302:
298:
297:
295:
294:
292:Jean Dieudonné
289:
283:
281:
275:
274:
263:
257:
256:
254:
253:
248:
243:
234:
232:
228:
227:
210:
206:
205:
199:
198:
196:
195:
190:Crafoord Prize
183:
174:
164:
162:
158:
157:
139:
138:Known for
135:
134:
132:
131:
126:
120:
118:
114:
113:
111:
110:
104:
100:
98:
94:
93:
83:
80:(aged 86)
73:
69:
68:
55:
44:
40:
39:
36:
28:
27:
24:
15:
9:
6:
4:
3:
2:
6421:
6410:
6407:
6405:
6402:
6400:
6397:
6395:
6392:
6390:
6387:
6385:
6382:
6380:
6377:
6375:
6372:
6370:
6367:
6365:
6362:
6360:
6357:
6355:
6352:
6350:
6347:
6345:
6342:
6340:
6337:
6336:
6334:
6319:
6315:
6311:
6309:
6301:
6300:
6297:
6287:
6284:
6282:
6279:
6277:
6274:
6272:
6271:Duminil-Copin
6268:
6267:
6265:
6260:
6257:
6255:
6252:
6250:
6247:
6245:
6241:
6240:
6238:
6233:
6230:
6228:
6225:
6223:
6220:
6218:
6214:
6213:
6211:
6206:
6203:
6201:
6198:
6196:
6193:
6191:
6190:Lindenstrauss
6187:
6186:
6184:
6179:
6176:
6174:
6171:
6169:
6166:
6164:
6160:
6159:
6157:
6152:
6149:
6147:
6143:
6142:
6140:
6135:
6132:
6130:
6127:
6125:
6122:
6120:
6116:
6115:
6113:
6108:
6105:
6103:
6100:
6098:
6095:
6093:
6089:
6088:
6086:
6081:
6078:
6076:
6073:
6071:
6068:
6066:
6062:
6061:
6059:
6054:
6051:
6049:
6046:
6044:
6040:
6039:
6037:
6032:
6029:
6027:
6024:
6022:
6018:
6017:
6015:
6010:
6007:
6005:
6002:
6000:
5997:
5995:
5991:
5990:
5988:
5983:
5980:
5978:
5974:
5973:
5971:
5966:
5963:
5961:
5958:
5956:
5953:
5951:
5947:
5946:
5944:
5939:
5936:
5934:
5931:
5929:
5926:
5924:
5920:
5919:
5917:
5912:
5909:
5907:
5903:
5902:
5900:
5895:
5892:
5890:
5886:
5885:
5883:
5878:
5875:
5873:
5869:
5868:
5866:
5861:
5858:
5856:
5852:
5851:
5849:
5844:
5841:
5839:
5835:
5834:
5832:
5831:
5827:
5823:
5816:
5811:
5809:
5804:
5802:
5797:
5796:
5793:
5787:
5784:
5782:
5779:
5777:
5774:
5771:
5769:
5766:
5763:
5760:
5757:
5754:
5751:
5747:
5744:
5740:
5738:
5735:
5733:
5729:
5728:David Mumford
5725:
5722:
5719:
5716:
5714:
5711:
5708:
5705:
5702:
5699:
5697:
5694:
5691:
5687:
5683:
5680:
5677:
5674:
5671:
5668:
5666:
5662:
5659:
5656:
5652:
5651:
5646:
5642:
5637:
5634:
5631:
5630:
5619:
5615:
5611:
5607:
5603:
5599:
5595:
5591:
5584:
5579:
5576:
5570:
5566:
5561:
5556:
5550:
5542:
5537:
5532:
5527:
5516:
5512:
5508:
5504:
5500:
5496:
5492:
5488:
5487:
5479:
5474:
5467:
5463:
5459:
5453:
5446:
5441:
5436:
5432:
5428:
5422:
5418:
5413:
5412:
5409:
5408:
5402:
5398:
5392:
5388:
5384:
5383:
5378:
5377:Ruelle, David
5374:
5369:
5364:
5360:
5356:
5354:
5348:
5344:
5333:
5329:
5325:
5320:
5313:
5309:
5302:
5297:
5293:
5289:
5282:
5277:
5273:
5269:
5262:
5257:
5253:
5247:
5243:
5242:
5236:
5229:
5222:
5221:
5215:
5211:
5205:
5201:
5197:
5192:
5180:
5175:
5171:
5164:
5160:
5156:
5152:
5146:
5142:
5137:
5131:
5127:
5123:
5122:
5119:
5113:
5109:
5108:
5103:
5099:
5095:
5091:
5087:
5083:
5079:
5070:
5065:
5064:
5058:
5054:
5047:
5043:
5039:
5034:
5027:
5022:
5018:
5014:
5013:
5005:
5001:
4997:
4996:
4993:
4992:
4987:
4983:
4976:
4971:
4966:
4962:
4958:
4957:
4949:
4945:
4941:
4940:David Mumford
4937:
4936:Allyn Jackson
4933:
4932:Michael Artin
4929:
4922:
4917:
4912:
4908:
4904:
4903:
4895:
4891:
4887:
4886:David Mumford
4883:
4882:Allyn Jackson
4879:
4878:Michael Artin
4875:
4874:
4853:
4849:
4842:
4834:
4828:
4820:
4814:
4810:
4803:
4787:
4783:
4777:
4762:
4758:
4752:
4744:
4738:
4734:
4733:
4725:
4717:
4710:
4702:
4701:
4693:
4685:
4679:
4675:
4674:
4666:
4658:
4651:
4642:
4634:
4628:
4624:
4623:
4615:
4607:
4601:
4597:
4596:
4588:
4581:
4577:
4573:
4567:
4563:
4559:
4558:
4553:
4547:
4545:
4536:
4530:
4526:
4521:
4520:
4511:
4503:
4497:
4493:
4492:
4484:
4476:
4474:0-387-97710-4
4470:
4466:
4462:
4461:Ieke Moerdijk
4458:
4452:
4450:
4443:, p. 22.
4442:
4437:
4426:
4422:
4418:
4411:
4404:
4398:, p. 21.
4397:
4392:
4385:
4380:
4373:
4369:
4365:
4358:
4339:
4332:
4328:
4322:
4315:
4310:
4303:
4298:
4291:
4286:
4278:
4274:
4268:
4261:
4257:
4251:
4249:
4232:
4228:
4222:
4206:
4202:
4196:
4180:
4176:
4170:
4162:
4158:
4151:
4135:
4131:
4130:The Spectator
4127:
4123:
4117:
4109:
4107:9780309164801
4103:
4099:
4098:
4093:
4087:
4079:
4075:
4068:
4066:
4057:
4053:
4047:
4038:
4033:
4024:
4019:
4012:
4007:
3996:
3995:
3987:
3980:
3979:Scharlau 2008
3975:
3956:
3949:
3942:
3923:
3916:
3910:
3895:
3891:
3885:
3878:(in Spanish).
3877:
3871:
3863:
3859:
3852:
3844:
3840:
3833:
3825:
3821:
3814:
3806:
3802:
3795:
3776:
3769:
3762:
3747:
3740:
3722:
3716:
3708:
3702:
3683:
3676:
3669:
3664:
3658:
3654:
3648:
3646:
3638:
3633:
3631:
3629:
3627:
3625:
3623:
3615:(3): 329â337.
3614:
3610:
3603:
3596:
3594:
3584:
3577:
3576:
3571:
3566:
3555:
3551:
3547:
3543:
3537:
3533:
3529:
3525:
3518:
3514:
3508:
3500:
3493:
3491:
3482:
3478:
3471:
3463:
3456:
3450:
3443:
3438:
3436:
3428:
3424:
3420:
3416:
3411:
3406:
3402:
3398:
3397:
3392:
3386:
3379:
3374:
3367:
3362:
3351:
3346:
3341:
3337:
3333:
3326:
3319:
3313:, "Foreword".
3312:
3307:
3305:
3295:
3290:
3283:
3275:
3271:
3264:
3248:
3244:
3238:
3236:
3228:
3224:
3219:
3212:
3211:
3204:
3202:
3194:
3193:
3186:
3179:
3178:
3171:
3169:
3167:
3165:
3157:
3152:
3145:
3144:Scharlau n.d.
3140:
3133:
3132:Scharlau 2008
3128:
3120:
3119:
3114:
3107:
3100:
3099:Jackson 2004a
3095:
3093:
3091:
3089:
3087:
3085:
3083:
3081:
3079:
3077:
3060:
3056:
3050:
3048:
3040:
3035:
3033:
3026:, p. 40.
3025:
3020:
3009:
3002:
2995:
2979:
2975:
2974:mathunion.org
2971:
2965:
2958:
2954:
2949:
2947:
2945:
2936:
2935:
2930:
2924:
2916:
2912:
2908:
2904:
2899:
2894:
2890:
2886:
2883:(7534): 272.
2882:
2878:
2874:
2870:
2866:
2860:
2851:
2846:
2842:
2835:
2833:
2831:
2823:
2822:Jackson 2004b
2818:
2816:
2814:
2812:
2810:
2808:
2800:
2799:Kleinert 2007
2795:
2793:
2791:
2783:
2778:
2776:
2768:
2763:
2761:
2759:
2751:
2746:
2744:
2742:
2740:
2738:
2736:
2728:
2724:
2719:
2712:
2711:Scharlau 2008
2707:
2705:
2703:
2701:
2699:
2697:
2695:
2693:
2691:
2686:
2672:
2668:
2667:Floris Takens
2664:
2660:
2654:
2647:
2644:Testimony by
2641:
2637:
2626:
2623:
2621:
2618:
2616:
2613:
2611:
2608:
2606:
2603:
2601:
2598:
2596:
2593:
2591:
2588:
2586:
2583:
2581:
2578:
2576:
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2555:
2552:
2550:
2547:
2545:
2542:
2539:
2536:
2530:
2527:
2525:
2522:
2520:
2517:
2515:
2514:Nuclear space
2512:
2510:
2507:
2504:
2501:
2495:
2494:Moduli scheme
2492:
2490:
2487:
2484:
2481:
2479:
2476:
2470:
2467:
2465:
2462:
2460:
2457:
2455:
2452:
2449:
2446:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2398:
2395:
2393:
2390:
2388:
2385:
2382:
2379:
2373:
2370:
2368:
2367:Delta-functor
2365:
2359:
2356:
2350:
2347:
2345:
2342:
2340:
2337:
2334:
2331:
2329:
2326:
2324:
2321:
2319:
2316:
2314:
2311:
2309:
2306:
2304:
2301:
2299:
2296:
2295:
2284:
2280:
2276:
2270:
2265:
2264:
2258:
2254:
2250:
2246:
2242:
2238:
2234:
2228:
2224:
2221:(in French).
2220:
2216:
2212:
2211:
2205:
2203:
2202:
2197:
2196:
2195:The Passenger
2191:
2186:
2185:
2181:
2177:
2173:
2168:
2165:
2163:
2162:Colonel Tears
2159:
2150:
2148:
2144:
2139:
2135:
2125:
2123:
2119:
2118:Chern classes
2115:
2111:
2107:
2103:
2099:
2094:
2092:
2088:
2084:
2080:
2076:
2072:
2068:
2063:
2061:
2057:
2053:
2049:
2045:
2041:
2037:
2033:
2023:
2021:
2017:
2013:
2009:
2005:
2001:
1997:
1993:
1988:
1985:
1981:
1977:
1972:
1970:
1966:
1955:
1953:
1948:
1943:
1938:
1936:
1932:
1931:David Mumford
1922:
1920:
1914:
1912:
1908:
1900:
1896:
1894:
1890:
1886:
1884:
1883:Tame topology
1881:
1879:
1875:
1871:
1868:
1865:Crystals and
1864:
1861:
1857:
1854:
1852:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1829:
1826:
1822:
1819:
1815:
1811:
1807:
1805:
1801:
1798:
1797:
1796:
1794:
1784:
1782:
1778:
1773:
1771:
1767:
1763:
1759:
1755:
1750:
1748:
1744:
1740:
1739:
1734:
1730:
1729:
1724:
1720:
1719:
1711:
1707:
1703:
1698:
1696:
1692:
1686:
1684:
1680:
1676:
1675:Galois theory
1672:
1671:number theory
1668:
1664:
1660:
1659:infinitesimal
1656:
1652:
1648:
1643:
1641:
1637:
1632:
1628:
1624:
1620:
1616:
1612:
1607:
1605:
1601:
1597:
1593:
1592:
1587:
1583:
1578:
1576:
1572:
1568:
1564:
1560:
1556:
1552:
1548:
1544:
1539:
1537:
1532:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1500:
1490:
1488:
1484:
1479:
1477:
1473:
1463:
1461:
1457:
1453:
1449:
1445:
1441:
1431:
1429:
1425:
1420:
1418:
1413:
1411:
1407:
1402:
1401:Pierre Lochak
1398:
1397:Leila Schneps
1394:
1383:
1379:
1377:
1372:
1370:
1365:
1361:
1356:
1352:
1348:
1345:
1340:
1338:
1333:
1328:
1324:
1323:Leila Schneps
1320:
1316:
1311:
1309:
1305:
1301:
1296:
1294:
1293:
1288:
1284:
1280:
1276:
1272:
1271:
1265:
1263:
1259:
1255:
1251:
1247:
1243:
1239:
1235:
1231:
1227:
1223:
1219:
1218:
1213:
1209:
1204:
1202:
1198:
1197:
1192:
1188:
1183:
1174:
1172:
1167:
1163:
1158:
1156:
1152:
1148:
1147:Pierre Samuel
1144:
1139:
1137:
1133:
1129:
1124:
1120:
1116:
1112:
1108:
1103:
1101:
1096:
1092:
1088:
1084:
1080:
1076:
1072:
1062:
1060:
1056:
1055:
1050:
1045:
1043:
1039:
1035:
1031:
1027:
1023:
1022:Galois theory
1019:
1015:
1011:
1007:
1004:, as well as
1003:
999:
995:
991:
990:
985:
981:
977:
973:
969:
965:
961:
957:
953:
952:number theory
949:
939:
937:
933:
929:
925:
924:David Mumford
921:
917:
913:
909:
905:
901:
897:
893:
892:Michael Artin
889:
886:theory), and
885:
881:
877:
873:
869:
868:group schemes
865:
860:
858:
853:
849:
845:
835:
833:
829:
825:
819:
814:
812:
811:Leila Schneps
808:
804:
800:
799:Yvonne Bruhat
796:
792:
788:
784:
780:
779:Pierre Samuel
774:
767:
765:
764:Oscar Zariski
761:
756:
754:
750:
746:
742:
738:
734:
729:
727:
726:Banach spaces
723:
719:
715:
710:
708:
704:
700:
696:
692:
688:
682:
676:
671:
669:
665:
655:
653:
648:
646:
641:
639:
635:
631:
627:
622:
620:
616:
611:
609:
605:
601:
597:
593:
592:Rieucros Camp
589:
579:
577:
573:
569:
565:
562:
558:
554:
549:
546:
542:
538:
534:
530:
526:
522:
507:
505:
501:
496:
492:
488:
484:
480:
476:
471:
469:
465:
461:
457:
453:
449:
445:
441:
440:mathematician
436:
425:
419:
409:
373:
369:
360:
354:
351:
349:
346:
344:
341:
339:
336:
334:
331:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
305:
303:
299:
293:
290:
288:
285:
284:
282:
280:
276:
269:
268:
264:
262:
258:
252:
249:
247:
244:
241:
240:scientifiques
236:
235:
233:
229:
226:
222:
218:
214:
211:
207:
204:
200:
191:
184:
182:
175:
173:
166:
165:
163:
159:
156:
152:
148:
147:number theory
144:
140:
136:
130:
127:
125:
122:
121:
119:
115:
108:
105:
102:
101:
99:
95:
90:
86:
74:
70:
66:
62:
58:
53:28 March 1928
45:
41:
34:
29:
22:
19:
5933:Grothendieck
5932:
5648:
5593:
5589:
5564:
5518:. Retrieved
5490:
5484:
5457:
5416:
5406:
5381:
5358:
5352:
5336:, retrieved
5332:the original
5328:Science News
5327:
5307:
5291:
5287:
5271:
5267:
5240:
5228:the original
5219:
5195:
5183:. Retrieved
5169:
5140:
5106:
5086:Illusie, Luc
5057:the original
5052:
5016:
5010:
4990:
4960:
4954:
4906:
4900:
4855:. Retrieved
4852:The Atlantic
4851:
4841:
4808:
4802:
4790:. Retrieved
4785:
4776:
4766:12 September
4764:. Retrieved
4760:
4751:
4731:
4724:
4715:
4709:
4699:
4692:
4672:
4665:
4656:
4650:
4641:
4621:
4614:
4594:
4587:
4555:
4518:
4510:
4490:
4483:
4464:
4436:
4425:the original
4420:
4416:
4403:
4391:
4379:
4371:
4367:
4357:
4345:. Retrieved
4321:
4314:Deligne 1998
4309:
4297:
4285:
4277:the original
4267:
4260:The Guardian
4235:. Retrieved
4231:the original
4221:
4209:. Retrieved
4195:
4185:12 September
4183:. Retrieved
4178:
4169:
4163:(in French).
4160:
4150:
4138:. Retrieved
4134:the original
4129:
4116:
4096:
4086:
4077:
4058:(in French).
4055:
4046:
4032:
4018:
4006:
3993:
3986:
3974:
3962:. Retrieved
3941:
3929:. Retrieved
3922:the original
3909:
3899:12 September
3897:. Retrieved
3894:www.mccme.ru
3893:
3884:
3870:
3861:
3857:
3851:
3842:
3838:
3832:
3823:
3819:
3813:
3804:
3800:
3794:
3782:. Retrieved
3761:
3749:. Retrieved
3744:Roy Lisker.
3739:
3729:15 September
3727:. Retrieved
3715:
3701:
3691:17 September
3689:. Retrieved
3675:
3663:
3637:Pragacz 2005
3612:
3608:
3583:
3573:
3569:
3565:
3523:
3507:
3498:
3480:
3470:
3461:
3449:
3400:
3394:
3390:
3385:
3373:
3361:
3335:
3331:
3318:
3282:
3273:
3263:
3251:. Retrieved
3246:
3218:
3209:
3191:
3185:
3176:
3151:
3139:
3127:
3121:(in French).
3116:
3106:
3063:. Retrieved
3059:the original
3039:Cartier 2001
3019:
2994:
2982:. Retrieved
2973:
2964:
2956:
2932:
2923:
2880:
2876:
2859:
2850:the original
2844:
2782:Cartier 2004
2767:Douroux 2012
2750:Cartier 2004
2718:
2653:
2640:
2308:AB5 category
2262:
2256:
2222:
2218:
2214:
2208:Publications
2201:Stella Maris
2199:
2193:
2187:
2175:
2169:
2166:
2161:
2157:
2156:
2131:
2095:
2064:
2048:topos theory
2029:
1989:
1973:
1961:
1949:
1945:
1940:
1928:
1918:
1915:
1906:
1904:
1823:Yoga of the
1792:
1790:
1774:
1766:finite field
1751:
1742:
1736:
1732:
1726:
1722:
1716:
1714:
1709:
1705:
1701:
1687:
1662:
1644:
1631:Armand Borel
1608:
1589:
1579:
1558:
1555:TĂŽhoku paper
1540:
1496:
1480:
1472:tuberculosis
1469:
1460:Algerian War
1437:
1424:Saint-Lizier
1421:
1414:
1389:
1380:
1375:
1373:
1368:
1364:Marthe Robin
1350:
1349:
1341:
1336:
1331:
1318:
1314:
1312:
1303:
1297:
1291:
1279:moduli space
1268:
1266:
1258:Fabien Morel
1249:
1245:
1215:
1208:Ronald Brown
1205:
1194:
1190:
1186:
1184:
1180:
1159:
1154:
1150:
1140:
1128:David Ruelle
1118:
1110:
1104:
1068:
1058:
1052:
1048:
1046:
993:
987:
945:
942:"Golden Age"
861:
851:
841:
821:
818:mathematics.
816:
768:
757:
753:TĂŽhoku paper
730:
711:
675:Henri Cartan
672:
661:
649:
642:
623:
612:
608:World War II
585:
582:World War II
550:
518:
479:Fields Medal
472:
456:sheaf theory
371:
367:
366:
265:
231:Institutions
202:
172:Fields Medal
85:Saint-Lizier
78:(2014-11-13)
18:
6359:Algebraists
6344:2014 deaths
6339:1928 births
6269:2022
6242:2018
6215:2014
6188:2010
6161:2006
6144:2002
6117:1998
6090:1994
6063:1990
6041:1986
6019:1982
5992:1978
5975:1974
5948:1970
5921:1966
5904:1962
5887:1958
5870:1954
5853:1950
5836:1936
5520:1 September
5501:: 930â941.
5458:zbMATH Open
5181:(in French)
4792:15 November
4718:. Springer.
4368:ScienceLine
4254:Phil Hoad,
4237:12 November
4140:26 December
4040:(in French)
4026:(in French)
4000:(in German)
3687:(in French)
3366:Schneps n.d
3253:14 November
3223:Ruelle 2007
3024:Ruelle 2007
2549:Quot scheme
2344:Chern class
1982:on which a
1969:ring theory
1549:theory and
1434:Citizenship
1417:Luc Illusie
1285:theory and
1123:Vietnam War
1087:Vietnam War
932:Barry Mazur
914:worked out
912:Jean Giraud
872:Luc Illusie
374:in French (
333:Luc Illusie
328:Jean Giraud
213:Mathematics
97:Nationality
6333:Categories
6232:Mirzakhani
6129:Kontsevich
5686:Tim Porter
5466:1129.01018
4857:5 December
4384:Leith 2004
4302:Serre 1955
4211:13 October
4122:Leith, Sam
3964:2 December
3784:25 January
3751:25 January
3294:1605.08112
3225:, p.
2869:Tate, John
2725:, p.
2681:References
2671:turbulence
2298:â-groupoid
2056:set theory
2032:cohomology
1952:Ravi Vakil
1874:derivators
1762:André Weil
1655:nilpotents
1615:Hirzebruch
1586:Jean Leray
1240:theory of
1075:pacifistic
838:IHĂS years
687:André Weil
640:in 1942.
541:Protestant
193:(declined)
49:1928-03-28
6286:Viazovska
6259:Venkatesh
6151:Voevodsky
6146:Lafforgue
6119:Borcherds
6043:Donaldson
5999:Fefferman
5906:Hörmander
5732:John Tate
5507:1088-9477
5435:801767784
5200:Gallimard
4944:John Tate
4890:John Tate
4827:cite book
3419:0040-8735
2984:5 January
2907:0028-0836
2392:DĂ©vissage
2372:Derivator
2004:algebraic
1935:John Tate
1925:Influence
1695:D-modules
1452:stateless
1327:MIT Press
900:Nick Katz
795:Jean Cerf
787:René Thom
588:Le Vernet
555:to evade
525:anarchist
141:Renewing
107:Stateless
6308:Category
6222:Bhargava
6168:Perelman
6163:Okounkov
6134:McMullen
6107:Zelmanov
6092:Bourgain
6065:Drinfeld
6053:Freedman
6048:Faltings
6026:Thurston
6004:Margulis
5977:Bombieri
5965:Thompson
5955:Hironaka
5855:Schwartz
5549:cite web
5515:34550461
5379:(2007).
5338:5 August
5312:archived
5161:(1998),
5044:(2004),
5002:(2001).
4975:Archived
4921:Archived
4554:(1977),
4463:(1992).
4347:29 April
4338:Archived
4205:Archived
4161:Le Monde
4094:(2006).
3955:Archived
3775:Archived
3554:Archived
3515:(2009).
3350:Archived
3118:Le Monde
3008:Archived
2978:Archived
2915:25592527
2871:(2015).
2454:K-theory
2397:DF-space
2291:See also
2259:(1973).
1958:Geometry
1887:Yoga of
1858:and the
1828:K-theory
1596:morphism
1531:L spaces
1483:landlady
1410:Pyrenees
1332:Survivre
1151:Survivre
976:K-theory
956:topology
852:de facto
826:and the
619:pensions
561:Lutheran
504:Pyrenees
500:Lasserre
491:K-theory
370:, later
151:topology
91:, France
6281:Maynard
6254:Scholze
6249:Figalli
6205:Villani
6200:Smirnov
6009:Quillen
5994:Deligne
5982:Mumford
5960:Novikov
5872:Kodaira
5860:Selberg
5843:Douglas
5838:Ahlfors
5663:at the
5618:0068874
5610:1969915
5185:2 April
4786:YouTube
4580:0463157
3931:17 June
3550:2490557
3427:0102537
3065:15 June
2885:Bibcode
2249:1315788
2241:0075539
2098:motives
1976:schemes
1937:wrote:
1856:Motives
1837:Schemes
1810:duality
1651:schemes
1487:commune
1136:Biology
1132:physics
1071:radical
984:schemes
596:Mendel.
568:Hamburg
545:Hamburg
502:in the
431:French:
414:German:
65:Germany
61:Prussia
6244:Birkar
6227:Hairer
6178:Werner
6124:Gowers
6102:Yoccoz
6080:Witten
6021:Connes
5923:Atiyah
5911:Milnor
5730:&
5616:
5608:
5571:
5513:
5505:
5464:
5433:
5423:
5393:
5248:
5206:
5147:
5114:
4815:
4739:
4680:
4629:
4602:
4578:
4568:
4531:
4498:
4471:
4104:
4052:"IMAG"
3548:
3538:
3425:
3417:
2913:
2905:
2877:Nature
2303:λ-ring
2283:886098
2281:
2271:
2247:
2239:
2229:
2108:, and
2042:, and
1725:) and
1617:. The
1536:Banach
1466:Family
1242:stacks
962:, and
916:torsor
906:, and
813:said:
805:, and
600:Hitler
564:pastor
557:Nazism
521:Berlin
489:, and
458:, and
272:(1953)
270:
261:Thesis
242:(IHĂS)
209:Fields
188:
179:
170:
161:Awards
89:AriĂšge
57:Berlin
6217:Avila
6097:Lions
6070:Jones
5950:Baker
5938:Smale
5928:Cohen
5877:Serre
5606:JSTOR
5586:(PDF)
5493:(8).
5481:(PDF)
5448:(PDF)
5315:(PDF)
5304:(PDF)
5284:(PDF)
5264:(PDF)
5231:(PDF)
5224:(PDF)
5166:(PDF)
5072:(PDF)
5060:(PDF)
5049:(PDF)
5007:(PDF)
4978:(PDF)
4951:(PDF)
4924:(PDF)
4897:(PDF)
4428:(PDF)
4413:(PDF)
4341:(PDF)
4334:(PDF)
3998:(PDF)
3958:(PDF)
3951:(PDF)
3925:(PDF)
3918:(PDF)
3860:[
3841:[
3822:[
3803:[
3778:(PDF)
3771:(PDF)
3724:(PDF)
3685:(PDF)
3605:(PDF)
3557:(PDF)
3520:(PDF)
3458:(PDF)
3353:(PDF)
3328:(PDF)
3289:arXiv
3011:(PDF)
3004:(PDF)
2661:in a
2632:Notes
2174:book
1842:Topoi
1754:Ă©tale
1547:sheaf
1503:Nancy
1355:deity
1095:Hanoi
1014:topos
553:Paris
6075:Mori
5894:Thom
5889:Roth
5569:ISBN
5555:link
5522:2011
5511:OCLC
5503:ISSN
5431:OCLC
5421:ISBN
5391:ISBN
5340:2008
5246:ISBN
5204:ISBN
5187:2014
5145:ISBN
5112:ISBN
4859:2022
4833:link
4813:ISBN
4794:2021
4768:2017
4737:ISBN
4678:ISBN
4627:ISBN
4600:ISBN
4566:ISBN
4529:ISBN
4496:ISBN
4469:ISBN
4349:2020
4239:2013
4213:2015
4187:2017
4142:2019
4102:ISBN
3966:2021
3933:2005
3901:2017
3786:2022
3753:2022
3731:2024
3693:2024
3536:ISBN
3415:ISSN
3255:2014
3067:2011
2986:2022
2911:PMID
2903:ISSN
2279:OCLC
2269:ISBN
2245:OCLC
2227:ISBN
2170:The
2065:The
2058:and
2018:and
2006:and
1990:His
1933:and
1907:yoga
1849:and
1802:and
1756:and
1627:Bonn
1509:and
1426:or
1399:and
1374:The
1260:and
1232:and
1171:CNRS
1145:and
1117:as "
1109:, a
1081:and
1073:and
1008:and
934:and
755:".
739:and
701:and
510:Life
186:1988
177:1977
168:1966
149:and
72:Died
43:Born
6276:Huh
6195:NgĂŽ
6173:Tao
6031:Yau
5598:doi
5462:Zbl
5363:doi
5021:doi
4965:doi
4911:doi
4525:115
3528:doi
3405:doi
3340:doi
2893:doi
2881:517
2192:'s
2188:In
1816:, "
1743:FGA
1733:SGA
1723:EGA
1710:FGA
1706:SGA
1702:EGA
1625:in
1557:" (
1517:of
1478:.
1304:EGA
1256:of
1164:at
1059:SGA
1049:EGA
994:EGA
910:).
898:),
870:),
830:in
809:),
762:by
728:).
654:".
523:to
6335::
5653:,
5647:,
5643:,
5614:MR
5612:.
5604:.
5594:61
5592:.
5588:.
5551:}}
5547:{{
5509:.
5497::
5491:55
5489:.
5483:.
5460:.
5429:.
5389:.
5385:.
5357:.
5349:.
5326:,
5292:51
5290:,
5286:,
5272:51
5270:,
5266:,
5202:.
5168:,
5100:;
5096:;
5092:;
5088:;
5084:;
5017:38
5015:.
5009:.
4973:.
4961:63
4959:.
4953:.
4942:;
4938:;
4934:;
4919:.
4907:63
4905:.
4899:.
4888:;
4884:;
4880:;
4850:.
4829:}}
4825:{{
4784:.
4759:.
4576:MR
4574:,
4560:,
4543:^
4527:.
4459:;
4448:^
4421:50
4419:.
4370:.
4366:.
4336:.
4329:.
4258:,
4247:^
4203:.
4177:.
4128:.
4076:.
4064:^
3953:.
3892:.
3773:.
3655:,
3644:^
3621:^
3613:46
3611:.
3607:.
3592:^
3572:,
3552:.
3546:MR
3544:.
3534:.
3522:.
3489:^
3460:.
3434:^
3423:MR
3421:,
3413:,
3348:.
3336:82
3334:.
3303:^
3245:.
3234:^
3227:35
3200:^
3163:^
3075:^
3046:^
3031:^
3006:.
2976:.
2972:.
2943:^
2931:.
2909:.
2901:.
2891:.
2879:.
2875:.
2867:;
2843:.
2829:^
2806:^
2789:^
2774:^
2757:^
2734:^
2689:^
2277:.
2243:.
2237:MR
2235:.
2223:16
2104:,
2093:.
2062:.
2038:,
2022:.
1891:,
1820:")
1708:,
1704:,
1677:,
1673:,
1642:.
1538:.
1430:.
1412:.
1264:.
1203:.
1173:.
1134:.
1102:.
958:,
954:,
950:,
930:,
926:,
878:,
834:.
801:,
797:,
793:,
789:,
785:,
781:,
697::
485:,
454:,
450:,
429:;
412:;
402:iË
396:Én
390:oÊ
223:,
219:,
215:â
87:,
63:,
59:,
5814:e
5807:t
5800:v
5748:"
5741:"
5692:.
5620:.
5600::
5557:)
5543:.
5533:.
5524:.
5468:.
5437:.
5399:.
5371:.
5365::
5254:.
5212:.
5189:.
5153:.
5132:.
5120:.
5074:.
5035:.
5029:.
5023::
4967::
4913::
4861:.
4835:)
4821:.
4796:.
4770:.
4745:.
4686:.
4635:.
4608:.
4537:.
4504:.
4477:.
4351:.
4316:.
4304:.
4292:.
4241:.
4215:.
4189:.
4144:.
4110:.
4080:.
4013:.
3968:.
3935:.
3903:.
3788:.
3755:.
3733:.
3695:.
3670:.
3639:.
3530::
3407::
3401:9
3380:.
3368:.
3342::
3297:.
3291::
3257:.
3229:.
3101:.
3069:.
3041:.
2988:.
2937:.
2917:.
2895::
2887::
2824:.
2801:.
2769:.
2752:.
2729:.
2727:7
2713:.
2285:.
2251:.
2160:(
1917:"
1812:(
1741:(
1731:(
1721:(
1302:(
1189:(
1057:(
992:(
902:(
894:(
408:/
405:k
399:d
393:t
387:r
384:ÉĄ
381:Ë
378:/
51:)
47:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.