• Corpus ID: 15050230

# 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…
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)
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
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
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).

## References

SHOWING 1-10 OF 36 REFERENCES
Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture
Abstract In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional
REMARKS ON A CONJECTURE OF FONTAINE AND MAZUR
• Richard Taylor
• Mathematics
Journal of the Institute of Mathematics of Jussieu
• 2002
We show that a continuous, odd, regular (non-exceptional), ordinary, irreducible, two-dimensional, \$l\$-adic representation of the absolute Galois group of the rational numbers is modular over some
On Serre's reciprocity conjecture for 2-dimensional mod p representations of the Galois group of Q
• Mathematics
• 2004
We first prove the existence of minimally ramified p-adic lifts of 2-dimensional mod p representations, that are odd and irreducible, of the absolute Galois group of Q,in many cases. This is
On Galois representations associated to Hilbert modular forms.
In this paper, we prove that, to any Hilbert cuspidal eigenform, one may attach a compatible system of Galois representations. This result extends the analogous results of Deligne and Deligne–Serre
Potentially semi-stable deformation rings
Let K/Qp be a finite extension and Gk = Gal(K/K) the Galois group of an alge braic closure K. Let F be a finite field of characteristic p, and Vf a finite dimensional F-vector space equipped with a
Sur les représentations \$p\$-adiques géométriques de conducteur 1 et de dimension 2 de \$G_{\Q}\$
We prove that there is no geometric \$p\$-adic representation of the Galois group of \$\Q\$ which is irreducible, of dimension 2, of conductor 1 and low weight, according to a conjecture of Fontaine and
Limites de représentations cristallines
• L. Berger
• Mathematics
Compositio Mathematica
• 2004
Let F be the fraction field of the ring of Witt vectors over a perfect field of characteristic p (for example \$F=\mathbb{Q}_p\$), and let GF be the absolute Galois group of F. The main result of this
Simple algebras, base change, and the advanced theory of the trace formula
• Mathematics
• 1989
A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups.
Multiplicity one Theorems
• Mathematics
• 2007
In the local, characteristic 0, non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We prove that such distributions are invariant by
Galois representations
— In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry,