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| Freitag E., Kiehl R. — Etale cohomology and the Weil conjecture |
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| Предметный указатель |
A-R category 120 122
A-R l-adic sheaf 123
Abhyankars Lemma 287
Acyclicity theorem 70
Admissible triangle 291
Associated bilinear form of a quadratic form 175 181
Base change, homomorphism 60
Base change, mapping 61
Base change, theorem for the direct image with proper support 91
Canonical flabby sheaf 23 129
Cartan’s lemma 23
Cech, cohomology groups 22
Cech, complex 22
Characteristic polynomial 157 159
Classification of nondegenerate double points 184
Classification of ordinary double points 187
Cohomological dimension of affine algebraic schemes 103
Cohomological dimension of the functor f! 94
Cohomological functor 293
Cohomology of a pencil of quadrics 208
Cohomology of quadrics 200 202 203
Cohomology with support on a closed subset 47
Cohomology, classes of algebraic cycles 150
Cohomology, groups with compact support 91
Compactifiable morphism 86
Compactification 86
Comparison of topological and algebraic variation 225 230 231
Comparison, theorem for algebraic and analytic variation 230
Conjecture of Hodge type 281
Conjecture of Lefschetz type 280
Constant sheaf 40
Constructible, sheaf 40
Constructible, sheaf of abelian groups 43
Construction of Henselian rings 16
Cover transformation group 283
Covering space 282
Cusp form 277
D(X. tor) 86
De La Vallee Poussin 274
Derived category 296
Derived direct image of a sheaf 27
Descent data 306
Direct image in the sense of Verdier 27
Direct image of a l-adic sheaf 128
Direct image of a sheaf 27
Direct image with proper support 90
Duality mapping 140
Effective descent data 307
Equivalence relation on sheaves 42
Et(X) for a scheme X 19
Etale, cohomology groups 13 20
Etale, covering 20
Etale, homomorphism 7
Etale, line bundle 24
Etale, morphism of schemes 18
Etale, neighbourhood 26
Etale, sheaf  associated to a quasicoherent sheaf M 20
Etale, sheaf  21
Etale, sheaf  21
Exact sequence for an open subscheme 92
Exactness of a sequence of sheaves 12
Excellent local rings 17
Ext(, ) 51
Extension of a sheaf by zero 81 84
Finite homomorphism 29
Finite ring homomorphism 15
Finitely generated local homomorphism 7
Finitely generated morphism of schemes 18
Finiteness theorem 95
Finiteness theorem for l-adic sheaves 128
Fixed point formula of Grothendieck and Nielsen — Wecken 257 164
Flabby sheaf 23
Flatness 9
Frobenius-homomorphism 161 163
Frobenius-morphism 162
Functor of sections with support in a closed subscheme 106
Fundamental character of the monodromy group 198
Fundamental estimate 259 264
Fundamental group 282
Fundamental lemma for the variation 209 232 245
G-sheaf 166 193
Galois cohomology 14
Galois covering space 283
Generators in the category of sheaves 13
Geometric Frobenius-homomorphism 163
Geometric point 25
Global Picard — Lefschetz formulas 251 253
Godement resolution 129
hadamard 274
Hard Lefschetz-theorem 274
Hecke operators 277
Henselian rings 15
Henselization 17
Hensel’ lemma 15
Injectives in the category of sheaves 13
Invariant characterization of the vanishing cycle 210
Inverse image of a sheaf 27 28
Kazhdan-Margulis 250
Kloostermann sum 276
| Kummer sequence 21
Kunneth formulas 99
l-adic sheaf 122
l-adic system 120
Lefschetz, embedding 177 179 180
Lefschetz, fixed point formula 157
Lefschetz, fixed point formula for the Frobenius-morphism 168
Lefschetz, pencils 175
Leray spectral sequence 28
Local etale homomorphism 8
Local smooth homomorphism 68
Locally constant l-adic sheaf 124 286
Locally constant sheaf 40 285
Locally noetherian category 44
Locally representable sheaf 35
Mapping cone 292
Mittag — Lefller condition 119
Mittag — Lemer — Artin — Rees condition 119
Mixed of weights  274
Moduli scheme 278
Monodromy, formalism 187
Monodromy, group 198
Monodromy, theory 175
Morphism of schemes 18
Neron model 279
Noetherian sheaf 43
Nondegenerate double point of a morphism 184
Nondegenerate quadratic form 175 181
Nondegenerately quadratically singular local homomorphism 183
Nonsingular quadratic form 176
Ordinary double point 176
Pencil of quadrics 205
Perfect complex 101 158
Permanence properties of etale morphisms 19
Permanence properties of etale ring extensions 10
Picard — Lefschetz formulas 187 199 247
Poincare duality 134 144
Point-wise pure 273
Presheaf on Et(X) 19
Principal congruence subgroup 276
Projective, limit of a projective system of schemes 49
Projective, system of schemes 48 49
Proper base change theorem 61
Purely inseparable morphism 33
Purity theorem 107
Quadratic form 175 181
Quadric 201
Quasifinite homomorphism 7 15
Quasifinite morphism of schemes 18
Quasiisomorphism 294
Quotient sheaf 12 13
Ramanujan conjecture 275 278
Ramification group 287
Rankin trick 264
Relative trace mapping 134 139
Representable sheaf 35
Reptesentablity lemma 34
Riemann existence theorem 286
Segre embedding 177
Sheaf of rational functions 54
Sheaf on Et(X) 19
Sheaf,  of abelian groups generated by a sheaf of sets 13
Sheaf, generated by a presheaf 12
Sheaves of  -vector spaces 131
Shift operator 292
Smooth algebra 68
Smooth base change theorem 70
Smooth homomorphism of strict Henelian rings 68
Smooth morphism of schemes 69
Spezialization, homomorphism 96
Spezialization, mapping 189 190
Stalk of a l-adic sheaf 124
Stalk of an etate presheaf 26
Standard conjectures on algebraic cycles 280
Strict Henselian rings 15
Strict Henselization 17
Strict local ring at a geometric point 26
Structure mapping 61
Support of a sheaf 26
Surjective mapping of sheaves 41
Tame fundamental group 289
Tamely ramified 288
Topological variation 219
Torsion sheaf 43
Trace mapping 133—135 139
Trace of an endomorphism of complexes 159
Trace of an endomorphism of G-moduls 160
Trace of an endomorphism of projective modules 157
Transcendental formalism of monodromy 210
Triple category 191 194
True endomorphism of an admissible triangle 159 160
Tsen’s theorem 14 15
Type S 137
Universal elliptic curve 278
Unramified homomorphism 7
Vanishing cycle 195 199
Variation 196 213 225 241
Weak Lefschetz theorem 106
Yoneda Ext 52
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