# Eigenvarieties for classical groups and complex conjugations in Galois representations

@inproceedings{Taibi2012EigenvarietiesFC,
title={Eigenvarieties for classical groups and complex conjugations in Galois representations},
author={Olivier Taibi},
year={2012}
}
• O. Taibi
• Published 1 March 2012
• Mathematics
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 GL2n+1 over a totally real number field F . We also extend it to the case of representations of GL2n/F whose multiplicative character is “odd”. We use a p-adic deformation argument, more precisely we prove that on the…
8 Citations

### Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality

Using the overconvergent cohomology modules introduced by Ash and Stevens, we construct eigenvarieties associated with reductive groups and establish some basic geometric properties of these spaces,

### On the image of complex conjugation in certain Galois representations

• Mathematics
Compositio Mathematica
• 2016
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

We prove a p-adic Labesse–Langlands transfer from the group of units in a definite quaternion algebra to its subgroup of norm one elements. More precisely, given an eigenvariety for the first group,

### Paquets stables des séries discrètes accessibles par endoscopie tordue; leur paramètre de Langlands

In this paper we gives the Langlands parameters of Langlands' packets of discrete series using the twisted endoscopy as explained by Arthur; this holds for orthogonal, symplectic, unitary and G-Spin

### Modularity of Galois Representations and Langlands Functoriality

• James Newton
• Mathematics, Art
Journal of the Indian Institute of Science
• 2022
This survey reports on some of the recent developments in the area of Galois representations and automorphic forms, with a particular focus on the author and Thorne’s work on symmetric power

### Overconvergent algebraic automorphic forms (Proc. London Math. Soc. 102 (2011) 193–228)

The purpose of this note is to describe and correct an unfortunate error in the author’s earlier paper [2]. These errors were apparently first noted by Olivier Täıbi in his forthcoming paper [3].

### Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations

• Mathematics
• 2019
In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real

### On subquotients of the étale cohomology of Shimura varieties

• Mathematics
Shimura Varieties
• 2020
We study the conditions imposed by conjectures of Arthur and Kottwitz on the Galois representations occurring in the cohomology of Shimura varieties.

## References

SHOWING 1-10 OF 53 REFERENCES

### The sign of Galois representations attached to automorphic forms for unitary groups

• Mathematics
Compositio Mathematica
• 2011
Abstract Let K be a CM number field and GK its absolute Galois group. A representation of GK is said to be polarized if it is isomorphic to the contragredient of its outer complex conjugate, up to a

### Construction of automorphic Galois representations, II

• Mathematics
• 2013
Recent developments in the theory of the stable trace formula, especially the proof by Laumon and Ngo of the fundamental lemma for unitary groups, has revived Langlands’ strategy for constructing

### Irreducibility of automorphic Galois representations of GL(n), n at most 5

• Mathematics
• 2011
Let pi be a regular, algebraic, essentially self-dual cuspidal automorphic representation of GL_n(A_F), where F is a totally real field and n is at most 5. We show that for all primes l, the l-adic

### Overconvergent algebraic automorphic forms

A general theory of overconvergent p‐adic modular forms and eigenvarieties is presented for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier

### On limit multiplicites of discrete series representations in spaces of automorphic forms

Of course the groups F, are then arithmetic subgroups of G. In this situation, it seems natural to assume that, as n-+ ~ , the spectral decomposition of L2(F,\G) will approximate that of G. In

### On the sign of regular algebraic polarizable automorphic representations

We remove a parity condition from the construction of automorphic Galois representations carried out in the Paris Book Project. We subsequently generalize this construction to the case of

### On torsion in the cohomology of locally symmetric varieties

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM

### Monodromy and local-global compatibility for l = p

We strengthen the compatibility between local and global Langlands correspondences for GL_{n} when n is even and l=p. Let L be a CM field and \Pi\ a cuspidal automorphic representation of

### Galois representations associated to holomorphic limits of discrete series

• Mathematics
Compositio Mathematica
• 2013
Abstract Generalizing previous results of Deligne–Serre and Taylor, Galois representations are attached to cuspidal automorphic representations of unitary groups whose Archimedean component is a

### Potential automorphy and change of weight

• Mathematics
• 2010
We prove an automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call \potentential diagonalizability." This result allows for \change of weight" and