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Real and Etale Cohomology : Lecture Notes in Computer Science - Claus Scheiderer

Real and Etale Cohomology

Lecture Notes in Computer Science

Paperback

Published: 27th October 1994
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This book makes a systematic study of the relations between the etale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, etale cohomology is cohomology of the real spectrum. It also contains new contributions in group cohomology and in topos theory. It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of etale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.

Introduction
Leitfaden
General notations and conventions
Real spectrum and real etale sitep. 1
Glueing etale and real etale sitep. 9
Limit theorems, stalks, and other basic factsp. 18
Some reminders on Weil restrictionsp. 30
Real spectrum of X and etale site of [actual symbol not reproducible]p. 42
The fundamental long exact sequencep. 56
Cohomological dimension of X[subscript b], I: Reduction to the field casep. 68
Equivariant sheaves for actions of topological groupsp. 87
Cohomological dimension of X[subscript b], II: The field casep. 96
G-toposesp. 107
Inverse limits of G-toposes: Two examplesp. 128
High degree cohomology of profinite groupsp. 143
Group actions on spaces: Topological versus topos-theoretic constructionsp. 161
Quotient topos of a G-topos, for G of prime orderp. 166
Comparison theoremsp. 173
Base change theoremsp. 180
Constructible sheaves and finiteness theoremsp. 191
Cohomology of affine varietiesp. 205
Relations to the Zariski topologyp. 212
Examples and complementsp. 219
Appendix A: Some complements on spectral spacesp. 245
Appendix B: Cohomology of Artin-Schreier structuresp. 251
Referencesp. 263
Symbol Indexp. 267
Subject Indexp. 272
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540584360
ISBN-10: 3540584366
Series: Lecture Notes in Computer Science
Audience: General
Format: Paperback
Language: English
Number Of Pages: 284
Published: 27th October 1994
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.65
Weight (kg): 0.44