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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A note on the cohomology of the Langlands group


Author: Edward S.T. Fan; with an appendix by M. Flach
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 11F75, 14F20; Secondary 20J06, 22A99
Published electronically: February 25, 2014
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Abstract: We begin with a comparison of various cohomology theories for topological groups. Using the continuity result for Moore cohomology, we establish a Hochschild-Serre spectral sequence for a slightly larger class of groups. We use these properties to compute the cohomology of the Langlands group of a totally imaginary field. The appendix answers a question raised by Flach concerning the cohomological dimension of the group $ \mathbb{R}$.


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Additional Information

Edward S.T. Fan
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: sfan@caltech.edu

M. Flach
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06230-2
PII: S 0002-9947(2014)06230-2
Keywords: Cohomology, topological groups, Langlands group
Received by editor(s): September 3, 2012
Received by editor(s) in revised form: June 12, 2013
Published electronically: February 25, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.