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Abhyankar's lemma

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Revêtements étales et groupe fondamental (SGA 1, Séminaire de Géométrie Algébriques du Bois-Marie 1960/61)
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Gold, Robert; Madan, M. L. (1978), "Some applications of Abhyankar's lemma",
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Allows one to kill tame ramification by taking an extension of a base field
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Cornell, Gary (1982), "On the Construction of Relative Genus Fields",
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Elementary and analytic theory of algebraic numbers
210:Transactions of the American Mathematical Society 115:More precisely, Abhyankar's lemma states that if 381: 53:but its sources remain unclear because it lacks 364: 19:Abhyankar's lemma is not directly related to 262: 371: 357: 288: 275: 239: 222: 112:by taking an extension of a base field. 84:Learn how and when to remove this message 206: 382: 323: 25: 13: 14: 421: 195:Finite extensions of local fields 327: 30: 390:Theorems in algebraic geometry 289:Narkiewicz, WĹ‚adysĹ‚aw (2004), 181:is an unramified extension of 1: 200: 405:Theorems in abstract algebra 343:. You can help Knowledge by 7: 188: 10: 426: 322: 106:Shreeram Shankar Abhyankar 18: 243:Mathematische Nachrichten 256:10.1002/mana.19780820112 162:is tamely ramified over 39:This article includes a 400:Algebraic number theory 68:more precise citations. 410:Abstract algebra stubs 339:-related article is a 236:. Theorem 3, page 504. 21:Abhyankar's conjecture 108:) allows one to kill 149:ramification indices 41:list of references 395:Lemmas in algebra 352: 351: 141:finite extensions 110:tame ramification 102:Abhyankar's lemma 94: 93: 86: 417: 373: 366: 359: 337:abstract algebra 331: 324: 315: 280: 279: 264:Grothendieck, A. 258: 235: 226: 89: 82: 78: 75: 69: 64:this article by 55:inline citations 34: 33: 26: 425: 424: 420: 419: 418: 416: 415: 414: 380: 379: 378: 377: 320: 305: 297:, p. 229, 295:Springer-Verlag 277:math.AG/0206203 224:10.2307/1998895 203: 191: 90: 79: 73: 70: 59: 45:related reading 35: 31: 24: 17: 12: 11: 5: 423: 413: 412: 407: 402: 397: 392: 376: 375: 368: 361: 353: 350: 349: 332: 318: 317: 303: 286: 260: 237: 217:(2): 501–511, 202: 199: 198: 197: 190: 187: 92: 91: 49:external links 38: 36: 29: 15: 9: 6: 4: 3: 2: 422: 411: 408: 406: 403: 401: 398: 396: 393: 391: 388: 387: 385: 374: 369: 367: 362: 360: 355: 354: 348: 346: 342: 338: 333: 330: 326: 325: 321: 314: 310: 306: 304:3-540-21902-1 300: 296: 292: 287: 284: 278: 273: 269: 265: 261: 257: 253: 249: 245: 244: 238: 234: 230: 225: 220: 216: 212: 211: 205: 204: 196: 193: 192: 186: 184: 180: 177: 173: 169: 165: 161: 157: 153: 150: 146: 142: 138: 134: 130: 126: 122: 118: 113: 111: 107: 104:(named after 103: 99: 88: 85: 77: 67: 63: 57: 56: 50: 46: 42: 37: 28: 27: 22: 345:expanding it 334: 319: 290: 267: 247: 241: 214: 208: 182: 178: 171: 167: 163: 159: 155: 151: 144: 136: 132: 129:local fields 124: 120: 116: 114: 101: 95: 80: 71: 60:Please help 52: 250:: 115–119, 174:, then the 98:mathematics 66:introducing 384:Categories 313:1159.11039 201:References 176:compositum 131:such that 266:(1971), 189:See also 170:divides 74:May 2024 233:1998895 147:, with 62:improve 311:  301:  283:p. 279 231:  158:, and 335:This 272:arXiv 229:JSTOR 47:, or 341:stub 299:ISBN 166:and 154:and 139:are 135:and 127:are 309:Zbl 252:doi 219:doi 215:271 143:of 96:In 386:: 307:, 281:, 248:82 246:, 227:, 213:, 185:. 179:AB 123:, 119:, 100:, 51:, 43:, 372:e 365:t 358:v 347:. 316:. 285:. 274:: 259:. 254:: 221:: 183:A 172:a 168:b 164:C 160:B 156:b 152:a 145:C 137:B 133:A 125:C 121:B 117:A 87:) 81:( 76:) 72:( 58:. 23:.

Index

Abhyankar's conjecture
list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
mathematics
Shreeram Shankar Abhyankar
tame ramification
local fields
finite extensions
ramification indices
compositum
Finite extensions of local fields
Transactions of the American Mathematical Society
doi
10.2307/1998895
JSTOR
1998895
Mathematische Nachrichten
doi
10.1002/mana.19780820112
Grothendieck, A.
arXiv
math.AG/0206203
p. 279
Springer-Verlag
ISBN

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