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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 caraiani@princeton.edu
Bao V. Le Hung
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA email lhvietbao@googlemail.com
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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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References

Arthur, J., The endoscopic classification of representations: orthogonal and symplectic groups, American Mathematical Society Colloquium Publications, vol. 61 (American Mathematical Society, Providence, RI, 2013).Google Scholar
Ash, A. and Stevens, G., Cohomology of arithmetic groups and congruences between systems of Hecke eigenvalues , J. reine angew. Math. 365 (1986), 192–220.Google Scholar
Borel, A. and Serre, J.-P., Corners and arithmetic groups , Comment. Math. Helv. 48 (1973), 436–491; avec un appendice: Arrondissement des variétés à coins, par A. Douady et L. Hérault.Google Scholar
Goresky, M., Harder, G. and MacPherson, R., Weighted cohomology , Invent. Math. 116 (1994), 139–213.Google Scholar
Harris, M., Lan, K.-W., Taylor, R. and Thorne, J., On the rigid cohomology of certain Shimura varieties, Preprint (2014), arXiv:1411.6717 [math.NT].Google Scholar
Harris, M. and Taylor, R., The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, vol. 151 (Princeton University Press, Princeton, NJ, 2001); with an appendix by V. G. Berkovich; MR 1876802 (2002m:11050).Google Scholar
Scholze, P., On torsion in the cohomology of locally symmetric varieties , Ann. of Math. (2) 185 (2015), 945–1066.Google Scholar
Taibi, O., Eigenvarieties for classical groups and complex conjugations in Galois representations, Math. Res. Lett., to appear. Preprint (2012), arXiv:1203.0225 [math.NT].Google Scholar
Taylor, R., The image of complex conjugation in l-adic representations associated to automorphic forms , Algebra Number Theory 6 (2012), 405–435.Google Scholar