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Leray's theorem

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477: 304: 366: 437: 410: 198: 170: 119: 68: 206: 146: 518: 386: 95: 547: 542: 312: 511: 552: 504: 537: 415: 391: 179: 151: 100: 49: 299:{\displaystyle {\check {H}}^{q}({\mathcal {U}},{\mathcal {F}})={\check {H}}^{q}(X,{\mathcal {F}}),} 71: 461: 24: 20: 40: 75: 36: 484: 128: 488: 371: 80: 531: 173: 476: 457: 122: 32: 451:
Lectures 16-17 from "Summer School 2000: Geometry of Toric Varieties."
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Cohomology of Line Bundles on Toric Varieties, Vanishing Theorems.
361:{\displaystyle {\check {H}}^{q}({\mathcal {U}},{\mathcal {F}})} 421: 397: 350: 340: 285: 244: 234: 185: 157: 106: 55: 456:
This article incorporates material from Leray's theorem on
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Relates abstract sheaf cohomology with Čech cohomology
418: 394: 374: 315: 209: 182: 154: 131: 103: 83: 52: 431: 404: 380: 360: 298: 192: 164: 140: 113: 89: 62: 462:Creative Commons Attribution/Share-Alike License 512: 176:on every finite intersection of elements of 8: 519: 505: 420: 419: 417: 396: 395: 393: 373: 349: 348: 339: 338: 329: 318: 317: 314: 284: 283: 268: 257: 256: 243: 242: 233: 232: 223: 212: 211: 208: 184: 183: 181: 156: 155: 153: 130: 105: 104: 102: 82: 54: 53: 51: 7: 473: 471: 14: 475: 432:{\displaystyle {\mathcal {U}}.} 412:with respect to the open cover 548:Theorems in algebraic topology 543:Theorems in algebraic geometry 460:, which is licensed under the 405:{\displaystyle {\mathcal {F}}} 388:-th Čech cohomology group of 355: 335: 323: 290: 274: 262: 249: 229: 217: 193:{\displaystyle {\mathcal {U}}} 165:{\displaystyle {\mathcal {F}}} 114:{\displaystyle {\mathcal {U}}} 63:{\displaystyle {\mathcal {F}}} 1: 491:. You can help Knowledge by 569: 470: 487:-related article is a 433: 406: 382: 362: 300: 194: 166: 142: 115: 91: 64: 553:Category theory stubs 434: 407: 383: 363: 301: 195: 167: 143: 116: 92: 65: 416: 392: 372: 313: 207: 180: 152: 129: 101: 81: 50: 447:Bonavero, Laurent. 35:) relates abstract 429: 402: 378: 358: 296: 190: 162: 141:{\displaystyle X.} 138: 111: 87: 60: 25:algebraic geometry 21:algebraic topology 500: 499: 381:{\displaystyle q} 326: 265: 220: 90:{\displaystyle X} 76:topological space 560: 521: 514: 507: 479: 472: 438: 436: 435: 430: 425: 424: 411: 409: 408: 403: 401: 400: 387: 385: 384: 379: 367: 365: 364: 359: 354: 353: 344: 343: 334: 333: 328: 327: 319: 305: 303: 302: 297: 289: 288: 273: 272: 267: 266: 258: 248: 247: 238: 237: 228: 227: 222: 221: 213: 199: 197: 196: 191: 189: 188: 171: 169: 168: 163: 161: 160: 147: 145: 144: 139: 120: 118: 117: 112: 110: 109: 96: 94: 93: 88: 69: 67: 66: 61: 59: 58: 37:sheaf cohomology 31:(so named after 568: 567: 563: 562: 561: 559: 558: 557: 528: 527: 526: 525: 485:category theory 468: 444: 414: 413: 390: 389: 370: 369: 316: 311: 310: 255: 210: 205: 204: 178: 177: 150: 149: 127: 126: 99: 98: 79: 78: 48: 47: 41:Čech cohomology 29:Leray's theorem 17: 12: 11: 5: 566: 564: 556: 555: 550: 545: 540: 530: 529: 524: 523: 516: 509: 501: 498: 497: 480: 453: 452: 443: 440: 428: 423: 399: 377: 357: 352: 347: 342: 337: 332: 325: 322: 307: 306: 295: 292: 287: 282: 279: 276: 271: 264: 261: 254: 251: 246: 241: 236: 231: 226: 219: 216: 187: 159: 137: 134: 108: 86: 57: 15: 13: 10: 9: 6: 4: 3: 2: 565: 554: 551: 549: 546: 544: 541: 539: 536: 535: 533: 522: 517: 515: 510: 508: 503: 502: 496: 494: 490: 486: 481: 478: 474: 469: 466: 465: 463: 459: 450: 446: 445: 441: 439: 426: 375: 345: 330: 320: 293: 280: 277: 269: 259: 252: 239: 224: 214: 203: 202: 201: 175: 135: 132: 124: 84: 77: 73: 44: 42: 38: 34: 30: 26: 22: 538:Sheaf theory 493:expanding it 482: 467: 455: 454: 448: 308: 45: 28: 18: 532:Categories 458:PlanetMath 442:References 200:, then 123:open cover 33:Jean Leray 324:ˇ 263:ˇ 218:ˇ 368:is the 309:where 174:acyclic 483:This 97:and 74:on a 72:sheaf 70:be a 46:Let 39:with 489:stub 148:If 23:and 172:is 125:of 121:an 19:In 534:: 43:. 27:, 520:e 513:t 506:v 495:. 464:. 427:. 422:U 398:F 376:q 356:) 351:F 346:, 341:U 336:( 331:q 321:H 294:, 291:) 286:F 281:, 278:X 275:( 270:q 260:H 253:= 250:) 245:F 240:, 235:U 230:( 225:q 215:H 186:U 158:F 136:. 133:X 107:U 85:X 56:F

Index

algebraic topology
algebraic geometry
Jean Leray
sheaf cohomology
Čech cohomology
sheaf
topological space
open cover
acyclic
PlanetMath
Creative Commons Attribution/Share-Alike License
Stub icon
category theory
stub
expanding it
v
t
e
Categories
Sheaf theory
Theorems in algebraic geometry
Theorems in algebraic topology
Category theory stubs

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