Knowledge (XXG)

Sheaf of spectra

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22: 217: 164: 51: 102: 258: 73: 34: 277: 251: 44: 38: 30: 106: 55: 282: 123: 244: 91: 228: 193: 174: 118: 271: 216: 224: 97:
is a contravariant functor from the category of open subsets of
15: 105:. A theorem of Jardine says that such presheaves form a 232: 170:
is then a fibrant/cofibrant object in that category.
126: 158: 43:but its sources remain unclear because it lacks 252: 173:The notion is used to define, for example, a 8: 117:is a weak equivalence if the induced map of 259: 245: 147: 131: 125: 103:good category of commutative ring spectra 101:, where morphisms are inclusions, to the 74:Learn how and when to remove this message 159:{\displaystyle \pi _{*}F\to \pi _{*}G} 7: 213: 211: 231:. You can help Knowledge (XXG) by 14: 215: 20: 140: 1: 192:Goerss, Paul (16 June 2008). 299: 210: 107:simplicial model category 86:In algebraic topology, a 29:This article includes a 177:in algebraic geometry. 58:more precise citations. 160: 166:is an isomorphism. A 161: 124: 88:presheaf of spectra 278:Algebraic topology 156: 31:list of references 240: 239: 92:topological space 84: 83: 76: 290: 261: 254: 247: 225:topology-related 219: 212: 204: 198: 168:sheaf of spectra 165: 163: 162: 157: 152: 151: 136: 135: 119:homotopy sheaves 79: 72: 68: 65: 59: 54:this article by 45:inline citations 24: 23: 16: 298: 297: 293: 292: 291: 289: 288: 287: 268: 267: 266: 265: 208: 196: 191: 188: 183: 143: 127: 122: 121: 80: 69: 63: 60: 49: 35:related reading 25: 21: 12: 11: 5: 296: 294: 286: 285: 283:Topology stubs 280: 270: 269: 264: 263: 256: 249: 241: 238: 237: 220: 206: 205: 187: 186:External links 184: 182: 179: 175:derived scheme 155: 150: 146: 142: 139: 134: 130: 82: 81: 39:external links 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 295: 284: 281: 279: 276: 275: 273: 262: 257: 255: 250: 248: 243: 242: 236: 234: 230: 227:article is a 226: 221: 218: 214: 209: 202: 201:TAG Lecture 2 195: 190: 189: 185: 180: 178: 176: 171: 169: 153: 148: 144: 137: 132: 128: 120: 116: 112: 108: 104: 100: 96: 93: 89: 78: 75: 67: 57: 53: 47: 46: 40: 36: 32: 27: 18: 17: 233:expanding it 222: 207: 200: 172: 167: 114: 110: 98: 94: 87: 85: 70: 61: 50:Please help 42: 56:introducing 272:Categories 181:References 64:March 2015 194:"Schemes" 149:∗ 145:π 141:→ 133:∗ 129:π 109:, where 52:improve 223:This 197:(PDF) 90:on a 37:, or 229:stub 274:: 199:. 41:, 33:, 260:e 253:t 246:v 235:. 203:. 154:G 138:F 115:G 113:→ 111:F 99:X 95:X 77:) 71:( 66:) 62:( 48:.

Index

list of references
related reading
external links
inline citations
improve
introducing
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topological space
good category of commutative ring spectra
simplicial model category
homotopy sheaves
derived scheme
"Schemes"
Stub icon
topology-related
stub
expanding it
v
t
e
Categories
Algebraic topology
Topology stubs

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