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Barsotti–Tate group

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508: 366: 394: 389: 405: 552: 63: 401: 384: 28: 326:
Barsotti, Iacopo (1962), "Analytical methods for abelian varieties in positive characteristic",
496: 446: 362: 477: 354: 536: 516: 489: 458: 415: 376: 335: 532: 528: 512: 485: 473: 465: 454: 411: 372: 350: 342: 331: 55: 47: 500: 441:, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 546: 470:
The crystals associated to Barsotti-Tate groups: with applications to abelian schemes
166: 17: 450: 523:
Tate, John T. (1967), "p-divisible groups.", in Springer, Tonny A. (ed.),
481: 358: 70:) under the name p-divisible groups, and named Barsotti–Tate groups by 434: 419: 472:, Lecture Notes in Mathematics, vol. 264, Berlin, New York: 349:, Lecture Notes in Mathematics, vol. 302, Berlin, New York: 136:
is (identified with) the group of elements of order divisible by
407:
Actes du Congrès International des Mathématiciens (Nice, 1970)
193:
are (represented by) a finite locally free scheme. The group
263:(or rather the group scheme corresponding to it). This is a 328:
Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962)
330:, Librairie Universitaire, Louvain, pp. 77–85, 62:) under the name equidimensional hyperdomain and by 410:, vol. 1, Gauthier-Villars, pp. 431–436, 501:"Groupes p-divisibles (d'après J. Tate), Exp. 318" 404:(1971), "Groupes de Barsotti-Tate et cristaux", 299:to be the subgroup scheme of elements of order 42:are similar to the points of order a power of 8: 154: 71: 525:Proc. Conf. Local Fields( Driebergen, 1966) 315:is the dimension of the Abelian variety. 241:is the direct limit of these subgroups. 59: 97:) to be an inductive system of groups 7: 82: 67: 435:"Barsotti-Tate groups and crystals" 201:for some locally constant function 25: 303:of an abelian variety. This is a 169:sheaf of commutative groups over 259:to be the cyclic group of order 181:-torsion, such that the points 157:defined a Barsotti–Tate group 509:Société Mathématique de France 347:Lectures on p-divisible groups 119:is a finite group scheme over 1: 287:-divisible group of height 1. 267:-divisible group of height 1. 307:-divisible group of height 2 89:-divisible group of height 390:Encyclopedia of Mathematics 569: 279:to be the group scheme of 54:. They were introduced by 383:Dolgachev, I.V. (2001) , 283:th roots of 1. This is a 507:, vol. 10, Paris: 433:de Jong, A. J. (1998), 402:Grothendieck, Alexander 439:Documenta Mathematica 229:) of points of order 527:, Berlin, New York: 233:is a scheme of rank 33:Barsotti–Tate groups 385:"P-divisible group" 155:Grothendieck (1971) 72:Grothendieck (1971) 511:, pp. 73–86, 505:Séminaire Bourbaki 497:Serre, Jean-Pierre 482:10.1007/BFb0058301 359:10.1007/BFb0060741 50:in characteristic 29:algebraic geometry 368:978-3-540-06092-5 40:-divisible groups 18:P-divisible group 16:(Redirected from 560: 553:Algebraic groups 539: 519: 492: 466:Messing, William 461: 429: 428: 427: 418:, archived from 397: 379: 343:Demazure, Michel 338: 153:More generally, 21: 568: 567: 563: 562: 561: 559: 558: 557: 543: 542: 529:Springer-Verlag 522: 495: 474:Springer-Verlag 464: 432: 425: 423: 400: 382: 369: 351:Springer-Verlag 341: 325: 322: 298: 278: 258: 247: 221:. The subgroup 149: 135: 118: 105: 93:(over a scheme 80: 48:abelian variety 23: 22: 15: 12: 11: 5: 566: 564: 556: 555: 545: 544: 541: 540: 520: 493: 462: 430: 398: 380: 367: 339: 321: 318: 317: 316: 294: 288: 274: 268: 254: 246: 243: 161:over a scheme 144: 131: 127:and such that 114: 110:≥0, such that 101: 79: 76: 24: 14: 13: 10: 9: 6: 4: 3: 2: 565: 554: 551: 550: 548: 538: 534: 530: 526: 521: 518: 514: 510: 506: 502: 498: 494: 491: 487: 483: 479: 475: 471: 467: 463: 460: 456: 452: 448: 444: 440: 436: 431: 422:on 2017-11-25 421: 417: 413: 409: 408: 403: 399: 396: 392: 391: 386: 381: 378: 374: 370: 364: 360: 356: 352: 348: 344: 340: 337: 333: 329: 324: 323: 319: 314: 310: 306: 302: 297: 293: 289: 286: 282: 277: 273: 269: 266: 262: 257: 253: 249: 248: 244: 242: 240: 236: 232: 228: 224: 220: 217:of the group 216: 212: 209:, called the 208: 204: 200: 197:(1) has rank 196: 192: 188: 185:(1) of order 184: 180: 176: 172: 168: 164: 160: 156: 151: 147: 143: 139: 134: 130: 126: 122: 117: 113: 109: 104: 100: 96: 92: 88: 84: 77: 75: 73: 69: 65: 61: 57: 53: 49: 45: 41: 39: 34: 30: 19: 524: 504: 469: 442: 438: 424:, retrieved 420:the original 406: 388: 346: 327: 312: 308: 304: 300: 295: 291: 284: 280: 275: 271: 264: 260: 255: 251: 238: 234: 230: 226: 222: 218: 214: 210: 206: 202: 198: 194: 190: 186: 182: 178: 177:-divisible, 174: 170: 162: 158: 152: 145: 141: 137: 132: 128: 124: 120: 115: 111: 107: 102: 98: 94: 90: 86: 81: 51: 43: 37: 36: 32: 26: 445:: 259–265, 83:Tate (1967) 426:2010-11-25 320:References 85:defined a 78:Definition 499:(1995) , 451:1431-0635 395:EMS Press 165:to be an 123:of order 547:Category 468:(1972), 345:(1972), 173:that is 56:Barsotti 537:0231827 517:1610452 490:0347836 459:1648076 416:0578496 377:0344261 336:0155827 245:Example 66: ( 58: ( 535:  515:  488:  457:  449:  414:  375:  365:  334:  311:where 237:, and 215:height 46:on an 290:Take 270:Take 250:Take 447:ISSN 363:ISBN 211:rank 167:fppf 106:for 68:1967 64:Tate 60:1962 478:doi 355:doi 213:or 205:on 189:of 140:in 35:or 27:In 549:: 533:MR 531:, 513:MR 503:, 486:MR 484:, 476:, 455:MR 453:, 443:II 437:, 412:MR 393:, 387:, 373:MR 371:, 361:, 353:, 332:MR 150:. 148:+1 74:. 31:, 480:: 357:: 313:d 309:d 305:p 301:p 296:n 292:G 285:p 281:p 276:n 272:G 265:p 261:p 256:n 252:G 239:G 235:p 231:p 227:n 225:( 223:G 219:G 207:S 203:h 199:p 195:G 191:G 187:p 183:G 179:p 175:p 171:S 163:S 159:G 146:n 142:G 138:p 133:n 129:G 125:p 121:S 116:n 112:G 108:n 103:n 99:G 95:S 91:h 87:p 52:p 44:p 38:p 20:)

Index

P-divisible group
algebraic geometry
abelian variety
Barsotti
1962
Tate
1967
Grothendieck (1971)
Tate (1967)
Grothendieck (1971)
fppf
MR
0155827
Demazure, Michel
Springer-Verlag
doi
10.1007/BFb0060741
ISBN
978-3-540-06092-5
MR
0344261
"P-divisible group"
Encyclopedia of Mathematics
EMS Press
Grothendieck, Alexander
Actes du Congrès International des Mathématiciens (Nice, 1970)
MR
0578496
the original
"Barsotti-Tate groups and crystals"

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