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On the image of complex conjugation in certain Galois representations

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  23 May 2016

Ana Caraiani  and
Bao V. Le Hung
Ana Caraiani
Affiliation:
Department of Mathematics, Princeton University, Fine Hall, Washington Rd., Princeton, NJ 08544, USA email [email protected]
Bao V. Le Hung
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA email [email protected]
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Abstract

We compute the image of any choice of complex conjugation on the Galois representations associated to regular algebraic cuspidal automorphic representations and to torsion classes in the cohomology of locally symmetric spaces for $\text{GL}_{n}$ over a totally real field $F$.

Keywords

Galois representationstorsion classeslocally symmetric spaceslocal–global compatibility

MSC classification

Primary: 11F80: Galois representations
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 7 , July 2016 , pp. 1476 - 1488
Copyright
© The Authors 2016 

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