# 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} }

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…

## 10 Citations

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### Modularity of Galois Representations and Langlands Functoriality

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## References

SHOWING 1-10 OF 43 REFERENCES

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

- MathematicsCompositio 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…

### Familles p-adiques de formes automorphes pour GLn

- Mathematics
- 2004

In this paper, we give definitions for p-adic automorphic forms on any twisted form of GLn/Q compact at infinity, and we construct the "eigenvariety" of finite slope eigenforms of wild level Γ0(p),…

### Overconvergent algebraic automorphic forms

- Mathematics
- 2011

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

- Mathematics
- 1986

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

- Mathematics
- 2013

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

- Mathematics
- 2013

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

- Mathematics
- 2014

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

- MathematicsCompositio 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…