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Cohomology of topological groups with applications to the Weil group

Published online by Cambridge University Press:  01 May 2008

M. Flach*
Affiliation:
Department of Mathematics, Caltech, Pasadena, CA 91125, USA (email: [email protected])
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Abstract

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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).

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

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