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Jardine J.F. — Generalized Etale Cohomology Theories
Jardine J.F. — Generalized Etale Cohomology Theories

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Название: Generalized Etale Cohomology Theories

Автор: Jardine J.F.

Аннотация:

A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 332

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Gamma$-space      147
$\Omega$-spectrum      3
Abstract norm map      85
Abstract transfer      88
Additive      223 287
Admissible filtration      274
Admissible function      19 25
Admissible path      19
Base change map      180
Big $\kappa$-site      236
Bilinear Inap      160 178
Bispectrum      1 7
Bonding maps      2 25 32
Bott periodic K-theory      265
Canonical composite      10
Canonical path      20 26
Cardinality of a scheme      231
cd-excision      286
cd-topology      282
Cech cohomology groups      213
Chaotic topology      55
Classifying topos      206
Cofibration      1 34 52 53 58
Cone      105 115
Covering family      282
Descent spectral sequence      201
Diagonal      24 29 100
Discrete G-module      209
Discrete G-set      205
Eilenberg — Mac Lane spectrurn      126
Finite descent      219
Function complex      5 36 52 58
G-world      211
Galois cohomology groups      213
Generalized Cech coho11101ogy groups      221
Generalized etale cohomology groups      199
Generalized Galois cohomology groups      221
Global bound      198
Global fibration      52 53
Global sections      210
Globally fibrant rnodel      54
Godenlent resolution      297
Grothendieck construction      147
Homotopy      166 172
Hypernonn      87 243
Hypertransfer      258
Induced field extension      265
inductor      259 265
Interchange condition      157
Join transformation      187
K-theory norm      144 192
K-theory presheaf      148 281
K-theory spectrum      149
Kall suspension      91 109
Kan spectrum      92 112
Local stable equivalence      53 59
Local weak equivalence      52
Locally trivial cofibration      63
Loop space      5
Loop spectrum      3 6
n-fold multilinear map      167 169
n-fold spectrum      25
Nisnevich topology      282
Norrnalized chain complex      97 127
Partial spectrum      8
Pointwise      52 198
Pointwise cofibration      43 60
Postnikov section      134 139 140
Postnikov tower      135
Presheaf of n-fold spectra      57
Presheaf of spectra      52
Projection formula      89 187
Pseudo join transformation      188
Pseudo-natural transformation      156
Realization functor      11
Rectification of a pseudo-functor      147
Separated etale site      278
Sheaf of stable homotopy groups      53
Simplicial spectrum      100
Singular functor      11
Smash product      18
Special $\Gamma$-space      164
Spectrum      2
Spectrum oject      121 122 130
Stabilization      40
Stable equivalence      1 9 11 42 47 131
Stable fibration      1 47
Stably fibrant      3 42
Stably fibrant model      76
Stably fibrant partial spectrum      9
Stably trivial      47
Stalkwise      52 198
Strict fibration      34 58
Strict weak equivalence      10 11 34 58 123 199
Strictly fibrant model      3
Suspension of a simplicial abelian group      116
Suspension spectrum      3 6 125
Tate spectral sequence      250
Telescope      11
TRANSFER      180 264
Trivial global fibration      63
Truncated n-fold spcetrum      49
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