Knowledge (XXG)

Weibel's conjecture

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389: 300: 185: 204: 430: 423: 90: 79: 68: 57: 46: 459: 416: 449: 104: 131: 37: 345: 317: 295:{\displaystyle K_{i}(X)=K_{i}(X\times \mathbb {A} ^{r}){\text{ for }}i\leq -d{\text{ and arbitrary }}r.} 191: 396: 354: 21: 454: 400: 364: 326: 376: 372: 111: 312: 25: 443: 388: 368: 89:
harvtxt error: no target: CITEREFCortiñasHaesemeyerSchlichtingWeibel2008 (
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Kerz, Moritz; Strunk, Florian; Tamme, Georg (2018), "Algebraic
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harvtxt error: no target: CITEREFGeisserHesselholt2010 (
404: 207: 134: 294: 179: 103:Weibel's conjecture asserts that for a Noetherian 74: 180:{\displaystyle K_{i}(X)=0{\text{ for }}i<-d} 67:harvtxt error: no target: CITEREFCisinski2013 ( 40:. Previously partial cases had been proven by 33: 315:(1980), "K-theory and analytic isomorphisms", 424: 45:harvtxt error: no target: CITEREFMorrow2016 ( 8: 56:harvtxt error: no target: CITEREFKelly2014 ( 20:gives a criterion for vanishing of negative 121:-groups vanish in degrees < − 431: 417: 358: 281: 264: 255: 251: 250: 234: 212: 206: 160: 139: 133: 63: 24:groups. The conjecture was proposed by 41: 29: 52: 7: 385: 383: 343:-theory and descent for blow-ups", 32:) and proven in full generality by 403:. You can help Knowledge (XXG) by 14: 387: 75:Geisser & Hesselholt (2010) 34:Kerz, Strunk & Tamme (2018) 261: 240: 224: 218: 151: 145: 1: 99:Statement of the conjecture 476: 382: 38:derived algebraic geometry 369:10.1007/s00222-017-0752-2 283: and arbitrary  460:Algebraic geometry stubs 346:Inventiones Mathematicae 318:Inventiones Mathematicae 190:and asserts moreover a 399:–related article is a 296: 194:property for negative 181: 86:Cortiñas et al. (2008) 297: 182: 205: 132: 192:homotopy invariance 36:using methods from 18:Weibel's conjecture 450:Algebraic geometry 397:algebraic geometry 331:10.1007/bf01390120 292: 177: 26:Charles Weibel 22:algebraic K-theory 412: 411: 284: 267: 163: 467: 433: 426: 419: 391: 384: 379: 362: 333: 301: 299: 298: 293: 285: 282: 268: 265: 260: 259: 254: 239: 238: 217: 216: 186: 184: 183: 178: 164: 161: 144: 143: 94: 83: 72: 61: 50: 16:In mathematics, 475: 474: 470: 469: 468: 466: 465: 464: 440: 439: 438: 437: 338: 313:Weibel, Charles 311: 308: 266: for  249: 230: 208: 203: 202: 162: for  135: 130: 129: 112:Krull dimension 101: 88: 77: 66: 64:Cisinski (2013) 55: 44: 12: 11: 5: 473: 471: 463: 462: 457: 452: 442: 441: 436: 435: 428: 421: 413: 410: 409: 392: 381: 380: 353:(2): 523–577, 335: 334: 325:(2): 177–197, 307: 304: 303: 302: 291: 288: 280: 277: 274: 271: 263: 258: 253: 248: 245: 242: 237: 233: 229: 226: 223: 220: 215: 211: 188: 187: 176: 173: 170: 167: 159: 156: 153: 150: 147: 142: 138: 100: 97: 13: 10: 9: 6: 4: 3: 2: 472: 461: 458: 456: 453: 451: 448: 447: 445: 434: 429: 427: 422: 420: 415: 414: 408: 406: 402: 398: 393: 390: 386: 378: 374: 370: 366: 361: 356: 352: 348: 347: 342: 337: 336: 332: 328: 324: 320: 319: 314: 310: 309: 305: 289: 286: 278: 275: 272: 269: 256: 246: 243: 235: 231: 227: 221: 213: 209: 201: 200: 199: 197: 193: 174: 171: 168: 165: 157: 154: 148: 140: 136: 128: 127: 126: 124: 120: 116: 113: 109: 106: 98: 96: 92: 87: 81: 76: 70: 65: 59: 54: 48: 43: 42:Morrow (2016) 39: 35: 31: 27: 23: 19: 405:expanding it 394: 350: 344: 340: 322: 316: 195: 189: 122: 118: 114: 107: 102: 53:Kelly (2014) 17: 15: 444:Categories 360:1611.08466 306:References 110:of finite 276:− 273:≤ 247:× 172:− 455:K-theory 198:-groups 377:3748313 84:, and 28: ( 375:  117:, the 105:scheme 395:This 355:arXiv 401:stub 169:< 91:help 80:help 69:help 58:help 47:help 30:1980 365:doi 351:211 327:doi 73:, 62:, 51:, 446:: 373:MR 371:, 363:, 349:, 323:61 321:, 125:: 95:. 432:e 425:t 418:v 407:. 367:: 357:: 341:K 329:: 290:. 287:r 279:d 270:i 262:) 257:r 252:A 244:X 241:( 236:i 232:K 228:= 225:) 222:X 219:( 214:i 210:K 196:K 175:d 166:i 158:0 155:= 152:) 149:X 146:( 141:i 137:K 123:d 119:K 115:d 108:X 93:) 82:) 71:) 60:) 49:)

Index

algebraic K-theory
Charles Weibel
1980
Kerz, Strunk & Tamme (2018)
derived algebraic geometry
Morrow (2016)
help
Kelly (2014)
help
Cisinski (2013)
help
Geisser & Hesselholt (2010)
help
Cortiñas et al. (2008)
help
scheme
Krull dimension
homotopy invariance
Weibel, Charles
Inventiones Mathematicae
doi
10.1007/bf01390120
Inventiones Mathematicae
arXiv
1611.08466
doi
10.1007/s00222-017-0752-2
MR
3748313
Stub icon

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