Overview

This book makes a systematic study of the relations between the tale cohomology of a scheme and the orderings of its residue fields. A major result is that in high degrees, tale 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 tale cohomology and Grothendieck sites. Independently, it is of interest to people working in the cohomology theory of groups or in topos theory.

Full Product Details

Author:   Claus Scheiderer
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1994 ed.
Volume:   1588
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.960kg
ISBN:  

9783540584360

ISBN 10:   3540584366
Pages:   284
Publication Date:   27 October 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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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