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Descent along torsors

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302: 155: 343: 122: 336: 263: 372: 329: 17: 362: 85:, since it says the "equivariant data" (which is an additional data) allows one to "descend" from 317: 245: 82: 8: 162: 43: 309: 269: 367: 273: 259: 181: 251: 105: 313: 255: 356: 234: 172:
to be the stack of quasi-coherent sheaves (in an appropriate topology). Then
188:; thus, the descent in this case says that to give an equivariant sheaf on 101: 235:"Notes on Grothendieck topologies, fibered categories and descent theory" 301: 287: 150:{\displaystyle \operatorname {Spec} L\to \operatorname {Spec} K} 32: 125: 149: 354: 288:Stack of Tannakian categories? Galois descent? 250:. Springer Studium Mathematik - Master. 2020. 53:says there is a canonical equivalence between 337: 344: 330: 232: 216: 14: 355: 233:Vistoli, Angelo (September 2, 2008). 296: 192:is to give a sheaf on the quotient 24: 81:-points. It is a basic example of 25: 384: 281: 300: 210: 135: 13: 1: 247:Algebraic Geometry I: Schemes 226: 157:, this generalizes classical 316:. You can help Knowledge by 7: 10: 389: 295: 168:For example, one can take 256:10.1007/978-3-658-30733-2 373:Algebraic geometry stubs 203: 27:In mathematics, given a 312:–related article is a 151: 152: 51:descent along torsors 123: 182:equivariant sheaves 163:field of definition 73:), the category of 61:), the category of 363:Algebraic geometry 310:algebraic geometry 147: 325: 324: 265:978-3-658-30732-5 16:(Redirected from 380: 346: 339: 332: 304: 297: 277: 241: 239: 220: 214: 156: 154: 153: 148: 106:Galois extension 21: 388: 387: 383: 382: 381: 379: 378: 377: 353: 352: 351: 350: 293: 284: 266: 244: 237: 229: 224: 223: 215: 211: 206: 124: 121: 120: 23: 22: 15: 12: 11: 5: 386: 376: 375: 370: 365: 349: 348: 341: 334: 326: 323: 322: 305: 291: 290: 283: 282:External links 280: 279: 278: 264: 242: 228: 225: 222: 221: 219:, Theorem 4.46 208: 207: 205: 202: 180:) consists of 159:Galois descent 146: 143: 140: 137: 134: 131: 128: 18:Galois descent 9: 6: 4: 3: 2: 385: 374: 371: 369: 366: 364: 361: 360: 358: 347: 342: 340: 335: 333: 328: 327: 321: 319: 315: 311: 306: 303: 299: 298: 294: 289: 286: 285: 275: 271: 267: 261: 257: 253: 249: 248: 243: 236: 231: 230: 218: 213: 209: 201: 199: 195: 191: 187: 183: 179: 175: 171: 166: 164: 160: 144: 141: 138: 132: 129: 126: 118: 114: 110: 107: 103: 99: 94: 92: 88: 84: 80: 77:-equivariant 76: 72: 68: 64: 60: 56: 52: 48: 45: 41: 37: 34: 30: 19: 318:expanding it 307: 292: 246: 217:Vistoli 2008 212: 197: 193: 189: 185: 177: 173: 169: 167: 158: 116: 112: 108: 104:of a finite 102:Galois group 97: 95: 90: 86: 78: 74: 70: 66: 65:-points and 62: 58: 54: 50: 46: 39: 35: 28: 26: 357:Categories 227:References 115:, for the 274:124918611 142:⁡ 136:→ 130:⁡ 368:Topology 119:-torsor 100:is the 83:descent 272:  262:  49:, the 42:and a 33:torsor 308:This 270:S2CID 238:(PDF) 204:Notes 161:(cf. 96:When 44:stack 314:stub 260:ISBN 139:Spec 127:Spec 252:doi 184:on 165:). 89:to 359:: 268:. 258:. 200:. 93:. 38:→ 345:e 338:t 331:v 320:. 276:. 254:: 240:. 198:G 196:/ 194:X 190:X 186:X 178:X 176:( 174:F 170:F 145:K 133:L 117:G 113:K 111:/ 109:L 98:G 91:Y 87:X 79:X 75:G 71:X 69:( 67:F 63:Y 59:Y 57:( 55:F 47:F 40:Y 36:X 31:- 29:G 20:)

Index

Galois descent
torsor
stack
descent
Galois group
Galois extension
field of definition
equivariant sheaves
Vistoli 2008
"Notes on Grothendieck topologies, fibered categories and descent theory"
Algebraic Geometry I: Schemes
doi
10.1007/978-3-658-30733-2
ISBN
978-3-658-30732-5
S2CID
124918611
Stack of Tannakian categories? Galois descent?
Stub icon
algebraic geometry
stub
expanding it
v
t
e
Categories
Algebraic geometry
Topology
Algebraic geometry stubs

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