Flach, M. (2008) Cohomology of topological groups with applications to the Weil group. Compositio Mathematica, 144 (03). pp. 633-656. ISSN 0010-437X. doi:10.1112/s0010437x07003338. https://resolver.caltech.edu/CaltechAUTHORS:20180809-133558024
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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).
| Item Type: | Article | ||||||
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| 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. | ||||||
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| Subject Keywords: | cohomology, topological groups, Weil group | ||||||
| Issue or Number: | 03 | ||||||
| Classification Code: | 2000 Mathematics Subject Classification 14F20 (primary), 11G40, 18F10, 22A99 (secondary) | ||||||
| DOI: | 10.1112/s0010437x07003338 | ||||||
| Record Number: | CaltechAUTHORS:20180809-133558024 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180809-133558024 | ||||||
| Official Citation: | Flach, M. (2008). Cohomology of topological groups with applications to the Weil group. Compositio Mathematica, 144(3), 633-656. doi:10.1112/S0010437X07003338 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 88710 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | George Porter | ||||||
| Deposited On: | 09 Aug 2018 20:54 | ||||||
| Last Modified: | 16 Nov 2021 00:29 |
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