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| Milne J.S. — Etale Cohomology. (PMS-33), Vol. 33 |
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| Ïðåäìåòíûé óêàçàòåëü |
AB3  5* 306
Action of sheaf 120
Acyclic morphism 232
Acyclic object 83 86
Affine morphism 4
Algebra; Azumaya 136—154
Algebra; central separable 141
Algebra; central simple 137;
Algebra; maximal etale sub- 139
Algebra; opposite 136
Algebraic space 116 122 157—159
Arithmetic genus 217
Artin character 186—187
Artin neighborhood 117
Artin — Schreier sequence 67
Artin — Schreier theory 127—128
Associated sheaf 57 60—62
Associated sheaf, stalk of 63
Azumaya algebra see algebra Azumaya
Bertini's theorem 209
Betti numbers 166 205
Bilinear 79
Branch locus 24
Branch locus, purity of 24
Brauer group 136—154
Brauer group of Henselian ring 138 148;
Brauer group of local ring 136—140
Brauer group of regular scheme 149
Brauer group of scheme 140—154;
Brauer group of smooth variety 149
Brauer group, cohomological 136 147
Brauer — Severi schemes 134—135
cartesian 144
Cartier divisor 73
Cartier dual 130
Cartier operator 129
Castelnuovo's criterion 217—219
Cayley — HamiHon polynomial 139
Char (X) 230
Chern class 204
Chern class, etale 271 -76
Chern class, total 273
Chern polynomial 273
Chern roots 274
Chow ring CH.(X) 274
Cofiltered category 305
Cofinal 306
Cohomoiogica! dimension 220—222 246 253—256 283
Cohomoiogica! dimension of curves 183- 84
Cohomology 84
Cohomology and inverse limits 88—89 119
Cohomology and Picard scheme 130—133
Cohomology of blowing-up 203 229—230 247
Cohomology of complete intersection 246
Cohomology of curves 175—197
Cohomology of direct limits 113
Cohomology of smooth group schemes 114—117
Cohomology of surfaces 197—219
Cohomology with compact support 93—94 229—230
Cohomology with support on Z 91 -94
Cohomology, Amitsur 97
Cohomology, Cech 95—105
Cohomology, Cech and derived 99 100 103 104—105
Cohomology, complex and etale 117—119 164 229 241
Cohomology, elate and flat 114—117
Cohomology, flat and Zariski 113—114
Cohomology, fmiteness of 222—227 232 244 246
Cohomology, invariance 224 231
Cohomology, nonabelian 122
Cohomology, of  106—110
Cohomology, of  245—246 270
Complex, bounded 310
Complex, double 309
Complex, perfect 263
Complex, total 309;
Conductor 188
Connected category 305
Construclible function 161
Cospecialization map 77 162 230
Covering of Picard type 126
Covering, E- 47
Covering, geometric 126;
Covering, infinitesimal 128—129
Covering, refinement of 95
Cycle map 268—271 275—276
Cycle, algebraic 268
Cycle, prime 268
Derived functor 82 310—312
Descent theory 16—20 158
Different 24 25
Direct image of presheaf 56—59
Direct image of sheaf 68—77
Direct image, higher 85 88
Direct image, higher with compact support 227—230
Discriminant 20 24
Elementary fibration 117
Etale closure 44
Etale morphism 3 22—35
Etale morphism of algebraic spaces 157
Etale morphism to normal scheme 29;
Etale morphism, standard 26 28
Etale morphism, topological in variance of 30
Etale neighborhood 36 38
Euler — Poincare characteristic 166 190—195 202 204—205
Exact 16 122
Excellent scheme 4
Excision 92
Extension by zero 76 78 81
Faithfully flat morphism 10—20
Faithfully flat morphism is strict epimorphism 16
Fibered category 144
Filtered category 305
Finite morphism 4—7
Flat morphism 3 7—20 31
Flat morphism is open 14
Formally etale 30
Formally smooth 30
Formally unramified 30
Frobenius elements, arithmetic 292;
Frobenius elements, geometric 292
Frobenius endomorphism 109 185
Fundamental class 247—252
Fundamental group 39—45
Fundamental group of curve 42—43 194
Fundamental group, tame 42 193—195 208
Fundamental group, true 45
Galois covering 40 43—44 49 99
Genencally locally constant 77
Generators, family of 83
Gerbe 144
Grodement resolution 90 171
Group scheme 52
Group scheme, Cartier dual 130
Gysin map 244 250 253 283—284
Gysin sequence 243—244 250—252
Hard Lefschetz theorem 207
Hasse — Witt matrix 128
Hensehzation 36
Henselian ring 3 32—39 41 239—240
Hensrl's lemma 32 35
Hilbert's theorem 90 124
Homotopic 167 257
Hypercohomology 310—312
Injective 82
Internal horn 79
Inverse image of presheaf 56—59
Inverse image of sheaf 68—76
Inverse image, in fibered category 144
Inverse image, preserves injectives 87
Inverse image, twisted 285
| Jacobian criterion 23
Jacobson scheme 65 90
Kazdan — Margulis theorem 211
Kuenneth formula 256—268 271—272
Kummer covering 41 42
Kummer sequence 66
Kummer theory 125—127
L 197
L-series 195—197 289—303
L-series, Artin 293 195—197
Lefschete trace formula 287—288 292 295 298
Lefschete trace formula for curves 185 195 205
Lefschetz pencils 197—199
Lefschetz theorems 207
Lefschetz theory, global 207—214
Lefschetz theory, local 199—207
Limits 304—306
Lisse 264
Map of degree r 167
Mapping cone 174
Mayer — Vietoris sequence 110
Milnor number 193
monodromy 207—211
Mordell — Weil theorem 133
Morphism of presheaves 48
Morphism of sheaves 50
Morphism of sites 56
Morphism of smooth S-pairs 241
Morphism, acyclic 232—241
Morphism, base change 223
Morphism, compactifiabie 227 229
Morphism, continuous 56
Morphism, Frobenius 290—291
Morphism, locally acyclic 232—241
Morphism, universally acyclic 232—241
Morphism, universally injective 25
Neron minimal model 192—193
Neron — Severi group 131—132 284
Neron — Severi group, finite, generation of 215—216
Normalization 4
Numerical equivalence 215 284
Ogg — Safarevic — Grothendieck formula 190—195
Ogg — Tate formula 193
Order 150
Pairing, canonical of Exts 167
Pairing, cup product 171—174
Perfect complex 263
Picard scheme 130—133
Picard — Lefechetz formula 206—207
Plurigenus 217
Poincare duality 276—286
Poincare duality, curves 175—185
Poincare duality, local 181—182
Presheaf 47
Presheaf, basically bounded 57
Presheaf, category of 48
Presheaf, constant 48
Presheaf, free 79;
Presheaf, section of 47
Presheaf, separated 49
Principal homogeneous space 120—133
Projection formula, cycles 268
Projection formula, sheaves 250
Proper base change theorem 72 89 222—227 260
Pseudofiltered 304- 305
Purity, cohomological 24!-47
Purity, of Azumaya algebras 153
Purity, of branch locus 24
Quasi-finite morphism 4—7
Quasi-isomorphism 310
Quaso-seciion 20
Riemann existence theorem 40 118
Riemann hypothesis 286
S,  ,  49
Separable, algebra 20
Separable, polynomial 22
Sheaf 49
Sheaf of  -vector spaces 164
Sheaf with finite stalks 155—156
Sheaf, 1-adic 163
Sheaf, category of 63
Sheaf, constant 65 156
Sheaf, constructive 155—156 160—164
Sheaf, etale over discrete valuation ring 75
Sheaf, etale over field 53
Sheaf, finite 155 -56
Sheaf, flabby 87—89 91 101—103 113
Sheaf, flasque 87
Sheaf, free 79
Sheaf, generieally locally constant 77
Sheaf, induced 90
Sheaf, locally constant 155 156 162
Sheaf, locally constructibie 160—164 225
Sheaf, locally free 563—564
Sheaf, Morsion 220
Sheaf, of  -modules 163
Sheaf, pseudo-coherent 80 95
Sheaf, represented by algebraic space 159
Sheaf, Tate twist of 163
Sheaf, torsion 220
Sheaf, twisted-constant 65 155 164
Sieve 55
Similar 137 141
Site 47 112—113
Skolem — Noether theorem 138 141
Smooth base change theorem 230—241
Smooth morphism 30 31 39
Smooth S-pair 241
Smooth specialization 230
Spectral sequence 307—309
Spectral sequence for closed subschemes 94
Spectral sequence with closed support 241;
Spectral sequence, Cech to derived 100—101
Spectral sequence, Hochschild — Serre 105
Spectral sequence, Leray 89 228;
Spectral sequence, local-global for Exts 91
Splits 139
STACK 144
Stalk 60 63—65 80
Stalk of direct image 70 71;
Stalk of higher direct image 88
Stalk of inverse image 69
Stein factorization 72
Strict epimorphism 16
Strict Henselization 38
Strictly coprime 32
Strictly Henselian (local) 3 38 41
Support of sheaf 75
Swan character 188
Tamely ramified 41—42
Tensor product, of complexes 257;
Tensor product, of sheaves 79
topology 47 54
Topology, comparison of 150—119
Tor-dimension 263
Torsor 120—133
Trace map 168—171 276 284
Trace map, noncommutative 301
Twisted forms 134
Universally injective morphism 25
Unrarmtied morphism 21 -32 36
Vanishing cycle 200
Vanishing cycle, canonical 205
Vanishing cycle, conjugacy of 208
Vanishing cycle, space of 207
Weak Lefschetz theorem 253—256
Weierstrass minimal equation 193
Weil Conjectures 286
Weil divisor 73
Zariski's main theorem 6
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