# On p-Adic Geometric Representations of G Q To

@inproceedings{Wintenberger2006OnPG, title={On p-Adic Geometric Representations of G Q To}, author={J.-P. Wintenberger}, year={2006} }

A conjecture of Fontaine and Mazur states that a geometric odd irreducible p-adic representation ρ of the Galois group of Q comes from a modular form ([10]). Dieulefait proved that, under certain hypotheses, ρ is a member of a compatible system of l-adic representations, as predicted by the conjecture ([9]). Thanks to recent results of Kisin ([15]), we are able to apply the method of Dieulefait under weaker hypotheses. This is useful in the proof of Serre’s conjecture ([20]) given in [11], [14…

## 6 Citations

On Serre's conjecture for 2-dimensional mod p representations of Gal( Q=Q)

- Mathematics
- 2009

We prove the existence in many cases of minimally ramied p-adic lifts of 2-dimensional continuous, odd, absolutely irreducible, mod p representations of the absolute Galois group of Q. It is…

On Serre's conjecture for mod l Galois representations over totally real fields

- Mathematics
- 2008

In 1987 Serre conjectured that any mod ' two-dimensional irre- ducible odd representation of the absolute Galois group of the rationals came from a modular form in a precise way. We present a…

Serre’s modularity conjecture (I)

- 2009

AbstractThis paper is the first part of a work which proves Serre’s modularity conjecture. We first prove the cases
$p\not=2$
and odd conductor, and p=2 and weight 2, see Theorem 1.2, modulo…

Modularity of Galois representations and motives with good reduction properties

- Mathematics
- 2007

This article consists of rather informal musings about relationships between Galois representations, motives and automorphic forms. These are occasioned by recent progress on Serre's conjecture in…

On the non-abelian global class field theory

- Mathematics
- 2013

AbstractLet $$K$$K be a global field. The aim of this speculative paper is to discuss the possibility of constructing the non-abelian version of global class field theory of $$K$$K by “glueing” the…

Serre’s modularity conjecture (II)

- Mathematics
- 2009

We provide proofs of Theorems 4.1 and 5.1 of Khare and Wintenberger (Invent. Math., doi:10.1007/s00222-009-0205-7, 2009).

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