Eigenvarieties for classical groups and complex conjugations in Galois representations

Olivier Taïbi (1, 2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 CMLS - Centre de Mathématiques Laurent Schwartz

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.

Mots clés: Eigenvarieties; Automorphic forms; Galois representations; Classical groups

Domaines: Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

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