Published May 2008
| public
Journal Article
Cohomology of topological groups with applications to the Weil group
- Creators
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Flach, M.
Chicago
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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
- Eprint ID
- 88710
- Resolver ID
- CaltechAUTHORS:20180809-133558024
- NSF
- DMS-0401403
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2018-08-09Created from EPrint's datestamp field
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2021-11-16Created from EPrint's last_modified field