Tamme G. — Introduction to Étale Cohomology :: Электронная библиотека попечительского совета мехмата МГУ

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Tamme G. — Introduction to Étale Cohomology

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Название: Introduction to Étale Cohomology

Автор: Tamme G.

Аннотация:

Étale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory. It has, in the last decades, brought fundamental new insights in arithmetic and algebraic geometric problems with many applications and many important results. The book gives a short and easy introduction into the world of Abelian Categories, Derived Functors, Grothendieck Topologies, Sheaves, General Étale Cohomology, and Étale Cohomology of Curves.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 186

Добавлена в каталог: 08.08.2007

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Предметный указатель

$(\mu_n)_X$       99
      64
$f^\ast, f_\ast$       87
      141
$\ell$ -torsion sheaf      150
$\partial$ -functor      9
$\partial$ -functor, morphism of $\partial$ -functors      10
$\partial$ -functor, universal      10
Abelian presheaf      25
Abelian sheaf      25
Additive category      3
Additive functor      4
Additive group      99
Adjoint      2 3
Adjoint, left adjoint      2
Amitsur complex      105
Artin spectral sequence      131
Artin — Schreier sequence      105
Associated sheaf      46
Base change      89 175 176
Big etale site      101
Brauer group      109
Brauer group, cohomological      113
Canonical injection      1
Canonical topology      26
Category      1
Category of abelian sheaves      50
Category of coverings      37
Category of left G-sets      27
Category, abelian category      4
Category, additive category      3
Category, filtered      19
Category, pseudo filtered      19
Cech cohomology      33 39
Cech cohomology, spectral sequence for      58
Cochains      56
Cohomological dimension      151
Cohomological dimension of algebraic schemes      174
Cohomological dimension of curves      163
Cohomological spectral sequence      14
Cohomology, Cech      33 39
Cohomology, cohomology group      54
Cohomology, etale      86
Cohomology, group cohomology      55 56
Cohomology, local      145
Cohomology, relative      145
Coimage      4
Cokernel      4
Comparison lemma      75 78
Comparison theorem      174
Constant sheaf      99
Constant sheaf, locally      151
Constructible sheaf      155
Continuous G-set      28
Covariant $\partial$ -functor      9
Coverings      24
Coverings, category of      37
Decomposition theorem      140
Derived functor      11
Direct image      64 87
Divisors, sheaf of      111
Dominating morphism      1
Edge morphism      14
Effaceable functor      10
Effective epimorphism      26
Epimorphism      1
Epimorphism, effective      26
Epimorphism, universal effective      26
Equivalence of categories      2
Equivalence of topologies      74
Etale, big etale site      101
Etale, cohomology      86
Etale, cohomology of curves      157
Etale, essentially etale algebra      121
Etale, morphism      85
Etale, neighbourhood      116
Etale, restricted etale site      90
Etale, site      86
Etale, topos      86
Exact, left exact      5
Exact, right exact      5
Exact, sequence      5
Exact, sequence of terms of low degrees      15
Extension of sheaves      91
Faithfull, fully      2
Filtered category      19
Filtration      13
Final sub category      20
Finitely presented morphism      90
Finiteness theorem      168 177
Five term exact sequence      15
Flabby sheaf      61
Flask sheaf      61
Flat morphism      85
Frobenius morphism      105
Fully faithful      2
functor      1
Functor,       64
Functor, $f^\ast, f_\ast$       87
Functor, $\partial$ -functor      9
Functor, additive      4
Functor, effaceable      10
Functor, isomorphism of functors      2
Functor, quasi-inverse      2
Functor, representable      3
Functor, right derived      11
Functor, spectral      14
G-set      27
G-set, continuous      28
Generator      7
Geometric point      114
Grothendieck topology      24
Henselian ring      121
Henselization      121
Henselization, strict      123
hilbert      90 107
Hochschild — Serre spectral sequence      72
Image      4
Image, direct      64 87
Image, inverse      65 87
Immersion      134
Induced G-module      66
Inductive limit      17
Inflation      72
Initial terms      13
Injective object      6
Injective object, sufficiently many      6

Injective resolution      11
Integral morphism      130
Inverse image      65 87
Isomorphism of functors      2
Kernel      4
Kummer sequence      109
Left adjoint      2
Left exact      5
Leray spectral sequence      70 71
LIMIT      17
Limit terms      13
Limit, inductive      17
Limit, projective      17
Local cohomology groups      145
Locally constant sheaf      151
Locally finitely presented morphism      85
Mapping cylinder      137
Monomorphism      1
Monomorphism, dominating monomorphism      1
Morphism of $\partial$ -functors      10
Morphism of functors      2
Morphism of spectral sequences      13
Morphism of topologies      24
Morphism, additive      4
Morphism, adjoint      2
Morphism, edge      14
Morphism, effective epimorphism      26
Morphism, epimorphism      1
Morphism, etale      85
Morphism, fiat      85
Morphism, finitely presented      90
Morphism, Frobenius      105
Morphism, integral      130
Morphism, locally finitely presented      85
Morphism, monomorphism      1
Morphism, quasi-compact      90
Morphism, quasi-separated      90
Morphism, universal effective epimorphism      26
Multiplicative group $(\mathbb{G}_m)_X$       99
Natural transformation      22
Noetherian topology      79
Picard group      107
Presheaf      23
Presheaf, abelian      25
Presheaf, representable      25
Presheaf, separated      47
PRODUCT      1
Projective limit      17
Projective limit of schemes      125
Pseudofiltered category      19
refinement      37
Relative cohomology groups      145
Relative cohomology sequence      145
Representable functor      3
Representable presheaf      25
Resolution      11
Restricted etale site      90
Restriction map      72
Restriction of sheaves      90 91
Right derived functor      11
Right exact      5
Separated presheaf      47
Sequence, Artin — Schreier      105
Sequence, exact      5
Sequence, exact sequence of low degree      15
Sequence, five term exact sequence      15
Sequence, Kummer      109
Sequence, relative cohomology      145
Sequence, spectral      13
Sequence, trivial spectral sequence      16
Shapiro’s Lemma      72
Sheaf      23
Sheaf of $\mathcal{O}_X$ -modules      100
Sheaf of divisors      111
Sheaf, $\ell$ -torsion      150
Sheaf, abelian      25 31
Sheaf, associated      46
Sheaf, constant      99
Sheaf, constructible      155
Sheaf, extension of      91
Sheaf, flabby      61
Sheaf, flask      61
Sheaf, locally constant      151
Sheaf, presheaf      23
Sheaf, restriction of      90
Sheaf, skyscraper      159
Sheaf, stalk      114
Sheaf, support of      120
Sheaf, torsion      146
Site      24
Site, etale      86
Site, restricted etale site      90
Skyscraper sheaf      159
Spectral functor      14
Spectral sequence      13
Spectral sequence for Cech cohomology      58
Spectral sequence, Artin      131
Spectral sequence, cohomological      14
Spectral sequence, exact sequence of low degree      15
Spectral sequence, Hochschild — Serre      72
Spectral sequence, initial terms      13
Spectral sequence, Leray      70 71
Spectral sequence, limit terms      13
Spectral sequence, morphism of      13
Spectral sequence, trivial      16
Stalk      114
Stalk of ${R^q}{f_\ast(F)}$       127
Strict Henselization      123
Strictly local ring      124
Subobject      1
Sufficiently many injective objects      6
Support      120
topology      23
Topology, canonical      26
Topology, covering      24
Topology, equivalence of topologies      74
Topology, Grothendieck topology      24
Topology, morphism of topologies      24
Topology, noetherian      79
Topos      86
Torsion sheaf      146
Torsion sheaf, $\ell$ -torsion      150
Transformation, natural      2
Transgression      72
Trivial spectral sequence      16
Universal $\partial$ -functor      10
Universal effective morphism      26
Vanishing of sheaves      135 143

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