Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-04T21:24:59.498Z Has data issue: false hasContentIssue false
  • English
  • Français

Cohomology of topological groups with applications to the Weil group

Part of: Topological and differentiable algebraic systems Categories and geometry (Co)homology theory Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 May 2008

M. Flach
M. Flach*
Affiliation:
Department of Mathematics, Caltech, Pasadena, CA 91125, USA (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild–Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-étale topology of a number ring recently introduced by Lichtenbaum (both with integer coefficients).

Keywords

cohomologytopological groupsWeil group

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 18F10: Grothendieck topologies 22A99: None of the above, but in this section
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 633 - 656
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The author is supported by grant DMS-0401403 from the National Science Foundation.