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Real and Etale Cohomology

  • Book
  • © 1994

Overview

Authors:
  1. Claus Scheiderer
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1588)

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Table of contents (19 chapters)

  1. Front Matter

    Pages I-XXIV
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  2. Real spectrum and real étale site

    • Claus Scheiderer
    Pages 1-8

  3. Glueing étale and real étale site

    • Claus Scheiderer
    Pages 9-17

  4. Limit theorems, stalks, and other basic facts

    • Claus Scheiderer
    Pages 18-29

  5. Some reminders on Weil restrictions

    • Claus Scheiderer
    Pages 30-41

  6. Real spectrum of X and étale site of \(X[\sqrt { - 1} ]\)

    • Claus Scheiderer
    Pages 42-55

  7. The fundamental long exact sequence

    • Claus Scheiderer
    Pages 56-67

  8. Cohomological dimension of X b , I: Reduction to the field case

    • Claus Scheiderer
    Pages 68-86

  9. Equivariant sheaves for actions of topological groups

    • Claus Scheiderer
    Pages 87-95

  10. Cohomological dimension of X b , II: The field case

    • Claus Scheiderer
    Pages 96-106

  11. G-toposes

    • Claus Scheiderer
    Pages 107-127

  12. Inverse limits of G-toposes: Two examples

    • Claus Scheiderer
    Pages 128-160

  13. Group actions on spaces: Topological versus topos-theoretic constructions

    • Claus Scheiderer
    Pages 161-165

  14. Quotient topos of a G-topos, for G of prime order

    • Claus Scheiderer
    Pages 166-172

  15. Comparison theorems

    • Claus Scheiderer
    Pages 173-179

  16. Base change theorems

    • Claus Scheiderer
    Pages 180-190

  17. Constructible sheaves and finiteness theorems

    • Claus Scheiderer
    Pages 191-204

  18. Cohomology of affine varieties

    • Claus Scheiderer
    Pages 205-211

  19. Relations to the Zariski topology

    • Claus Scheiderer
    Pages 212-218

  20. Examples and complements

    • Claus Scheiderer
    Pages 219-243
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Keywords

About this book

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

Bibliographic Information

  • Book Title: Real and Etale Cohomology

  • Authors: Claus Scheiderer

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0074269

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-58436-0Published: 27 October 1994

  • eBook ISBN: 978-3-540-48797-5Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XXIV, 284

  • Topics: Algebraic Geometry, K-Theory, Group Theory and Generalizations

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