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Foundations of Algebraic Geometry

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In the 1950s Weil's work was one of several competing attempts to provide satisfactory foundations for algebraic geometry, all of which were superseded by
17: 326: 79: 282: 146: 28: 97:. (It was not known at the time that Jacobians are always projective varieties.) It was some time before anyone found any examples of 260: 171: 225: 359: 344: 166: 252: 217: 349: 354: 251:, American Mathematical Society Colloquium Publications, vol. 29 (2 ed.), Providence, R.I.: 60: 121: 105: 313: 291: 270: 235: 192: 159: 109: 8: 216:, American Mathematical Society Colloquium Publications, vol. 29, Providence, R.I.: 94: 64: 56: 295: 196: 90: 52: 256: 221: 200: 138: 304: 299: 180: 98: 86: 309: 266: 246: 231: 211: 188: 155: 75: 134: 338: 277: 242: 207: 40: 74:
Weil was motivated by the need for a rigorous theory of correspondences on
169:(1971), "The foundation of algebraic geometry from Severi to André Weil", 184: 68: 78:
in positive characteristic, which he used in his proof of the
280:(1948), "Book Review: Foundations of algebraic geometry", 67:
by defining the local intersection multiplicity of two
139:"AndrĂ© Weil and the foundations of algebraic geometry" 336: 80:Riemann hypothesis for curves over finite fields 63:. In particular it gives a careful treatment of 165: 283:Bulletin of the American Mathematical Society 147:Notices of the American Mathematical Society 303: 276: 133: 14: 337: 93:partly so that he could construct the 172:Archive for History of Exact Sciences 29:Fondements de la GĂ©ometrie AlgĂ©brique 241: 206: 48: 44: 24: 27:For the book by Grothendieck, see 25: 371: 329:Foundations of Algebraic Geometry 320: 248:Foundations of Algebraic Geometry 213:Foundations of Algebraic Geometry 36:Foundations of Algebraic Geometry 18:Foundations of algebraic geometry 167:van der Waerden, Bartel Leendert 305:10.1090/S0002-9904-1948-09040-1 13: 1: 327:Extracts from the preface of 253:American Mathematical Society 218:American Mathematical Society 127: 7: 115: 101:that are not projective. 99:complete abstract varieties 10: 376: 26: 360:History of mathematics 345:1946 non-fiction books 122:Weil cohomology theory 91:projective varieties 296:1948Sci...107...75W 95:Jacobian of a curve 65:intersection theory 350:Algebraic geometry 185:10.1007/BF00357215 108:'s development of 53:algebraic geometry 355:Mathematics books 262:978-0-8218-1029-3 16:(Redirected from 367: 316: 307: 273: 238: 203: 162: 143: 85:Weil introduced 76:algebraic curves 51:) that develops 21: 375: 374: 370: 369: 368: 366: 365: 364: 335: 334: 323: 263: 228: 141: 135:Raynaud, Michel 130: 118: 32: 23: 22: 15: 12: 11: 5: 373: 363: 362: 357: 352: 347: 333: 332: 322: 321:External links 319: 318: 317: 290:(7): 671–675, 278:Zariski, Oscar 274: 261: 239: 226: 204: 179:(3): 171–180, 163: 154:(8): 864–867, 129: 126: 125: 124: 117: 114: 61:characteristic 41:AndrĂ© Weil 9: 6: 4: 3: 2: 372: 361: 358: 356: 353: 351: 348: 346: 343: 342: 340: 331: 330: 325: 324: 315: 311: 306: 301: 297: 293: 289: 285: 284: 279: 275: 272: 268: 264: 258: 254: 250: 249: 244: 240: 237: 233: 229: 227:9780821874622 223: 219: 215: 214: 209: 205: 202: 198: 194: 190: 186: 182: 178: 174: 173: 168: 164: 161: 157: 153: 149: 148: 140: 136: 132: 131: 123: 120: 119: 113: 111: 107: 102: 100: 96: 92: 88: 83: 81: 77: 72: 70: 66: 62: 58: 54: 50: 46: 42: 39:is a book by 38: 37: 30: 19: 328: 287: 281: 247: 212: 176: 170: 151: 145: 106:Grothendieck 103: 89:rather than 84: 73: 69:subvarieties 35: 34: 33: 243:Weil, AndrĂ© 208:Weil, AndrĂ© 339:Categories 128:References 201:189787203 245:(1962), 210:(1946), 137:(1999), 116:See also 87:abstract 314:1565074 292:Bibcode 271:0144898 236:0023093 193:1554142 160:1704257 110:schemes 59:of any 43: ( 312:  269:  259:  234:  224:  199:  191:  158:  57:fields 197:S2CID 142:(PDF) 55:over 257:ISBN 222:ISBN 49:1962 45:1946 300:doi 181:doi 341:: 310:MR 308:, 298:, 288:54 286:, 267:MR 265:, 255:, 232:MR 230:, 220:, 195:, 189:MR 187:, 175:, 156:MR 152:46 150:, 144:, 112:. 82:. 71:. 47:, 302:: 294:: 183:: 177:7 31:. 20:)

Index

Foundations of algebraic geometry
Fondements de la Géometrie Algébrique
André Weil
1946
1962
algebraic geometry
fields
characteristic
intersection theory
subvarieties
algebraic curves
Riemann hypothesis for curves over finite fields
abstract
projective varieties
Jacobian of a curve
complete abstract varieties
Grothendieck
schemes
Weil cohomology theory
Raynaud, Michel
"André Weil and the foundations of algebraic geometry"
Notices of the American Mathematical Society
MR
1704257
van der Waerden, Bartel Leendert
Archive for History of Exact Sciences
doi
10.1007/BF00357215
MR
1554142

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