Lecture Notes in Mathematics

By: Claus Scheiderer

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Paperback | 27 October 1994

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308 Pages

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23.39 x 15.6 x 1.65

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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.

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Non-Fiction Mathematics Geometry Algebraic Geometry Groups & Group Theory Algebra Topology Algebraic Topology

Introduction
Leitfaden
General notations and conventions
Real spectrum and real etale site	p. 1
Glueing etale and real etale site	p. 9
Limit theorems, stalks, and other basic facts	p. 18
Some reminders on Weil restrictions	p. 30
Real spectrum of X and etale site of [actual symbol not reproducible]	p. 42
The fundamental long exact sequence	p. 56
Cohomological dimension of X[subscript b], I: Reduction to the field case	p. 68
Equivariant sheaves for actions of topological groups	p. 87
Cohomological dimension of X[subscript b], II: The field case	p. 96
G-toposes	p. 107
Inverse limits of G-toposes: Two examples	p. 128
High degree cohomology of profinite groups	p. 143
Group actions on spaces: Topological versus topos-theoretic constructions	p. 161
Quotient topos of a G-topos, for G of prime order	p. 166
Comparison theorems	p. 173
Base change theorems	p. 180
Constructible sheaves and finiteness theorems	p. 191
Cohomology of affine varieties	p. 205
Relations to the Zariski topology	p. 212
Examples and complements	p. 219
Appendix A: Some complements on spectral spaces	p. 245
Appendix B: Cohomology of Artin-Schreier structures	p. 251
References	p. 263
Symbol Index	p. 267
Subject Index	p. 272
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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