# 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…

## 8 Citations

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### Modularity of Galois Representations and Langlands Functoriality

- Mathematics, ArtJournal of the Indian Institute of Science
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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)

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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

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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

- 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…

### 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…

### 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…