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Published May 2008 | public
Journal Article

Cohomology of topological groups with applications to the Weil group

Flach, M.

Abstract

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).

Additional Information

© Foundation Compositio Mathematica 2008. Received 7 October 2006, accepted in final form 1 October 2007. The author is supported by grant DMS-0401403 from the National Science Foundation. I am very grateful to Steve Lichtenbaum for extremely stimulating discussions about Weil-étale cohomology and for inviting me to speak at Brown University. I would also like to thank Thomas Geisser for many discussions related to topos theory, in particular concerning Proposition 7.1 above.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023