Eigenvarieties for classical groups and complex conjugations in Galois representations

Abstract : The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual, cuspidal automorphic representations of $\GL_{2n+1}$ over a totally real number field $F$. We also extend it to the case of representations of $\GL_{2n}/F$ whose multiplicative character is ''odd''. We use a $p$-adic deformation argument, more precisely we prove that on the eigenvarieties for symplectic and even orthogonal groups, there are ''many'' points corresponding to (quasi-)irreducible Galois representations. The recent work of James Arthur describing the automorphic spectrum for these groups is used to define these Galois representations, and also to transfer self-dual automorphic representations of the general linear group to these classical groups.
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https://hal.archives-ouvertes.fr/hal-00675682
Contributor : Olivier Taïbi <>
Submitted on : Thursday, March 1, 2012 - 4:53:37 PM
Last modification on : Tuesday, April 2, 2019 - 2:15:30 PM
Document(s) archivé(s) le : Thursday, May 31, 2012 - 2:45:47 AM

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• HAL Id : hal-00675682, version 1
• ARXIV : 1203.0225

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Olivier Taïbi. Eigenvarieties for classical groups and complex conjugations in Galois representations. 2012. ⟨hal-00675682⟩

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