Real and étale cohomology
著者
書誌事項
Real and étale cohomology
（Lecture notes in mathematics, 1588）
Springer-Verlag, c1994
- : gw
- : us
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注記
Includes bibliographical references (p. [263])-266) and symbol and subject indexes
内容説明・目次
内容説明
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.
目次
Real spectrum and real etale site.- Glueing etale and real etale site.- Limit theorems, stalks, and other basic facts.- Some reminders on Weil restrictions.- Real spectrum of X and etale site of .- The fundamental long exact sequence.- Cohomological dimension of X b , I: Reduction to the field case.- Equivariant sheaves for actions of topological groups.- Cohomological dimension of X b , II: The field case.- G-toposes.- Inverse limits of G-toposes: Two examples.- Group actions on spaces: Topological versus topos-theoretic constructions.- Quotient topos of a G-topos, for G of prime order.- Comparison theorems.- Base change theorems.- Constructible sheaves and finiteness theorems.- Cohomology of affine varieties.- Relations to the Zariski topology.- Examples and complements.
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