Résumé We prove Breuil's conjecture concerning the reduction modulo $ p $ of trianguline
representations $ V $ and of the representations $\Pi (V) $ of $\mathrm {GL} _2 (\mathbf {Q} …

We prove Breuil's conjecture concerning the reduction modulo $ p $ of trianguline
representations $ V $ and of the representations $\Pi (V) $ of $\mathrm {GL} _2 (\mathbf {Q} …

On démontre la conjecture de Breuil concernant la réduction modulo p des représentations
triangulines V et des représentations H (V) de GL2 (Qp) qui leur sont associées par la …

Let L be a finite extension of Qp. We construct a (p-adic local Langlands) correspondence
attaching to any irreducible, 2-dimensional, L-representation of GQp, a unitary, admissible …

Two deep theories were independently developped this last 50 years in number theory, the
p-adic theory of Fontaine and the theory of automorphic representations by Langlands …

Abstract (The p-adic local Langlands correspondence for GL2 (Qp)) The p-adic local
Langlands correspondence for GL2 (Qp) is a bijection between some 2-dimensional …

This thesis deals with two problems within the Langlands program. For the first problem,
inthesituationofGL2 andanon-minuscule cocharacter, we provide a counter-example (under …

Let Π be a unitary representation of GL2 (Qp), topologically of finite length. We describe the
sub-representation Πan made of its locally analytic vectors, and its filtration by radius of …

The goal of my talk was to explain some recent progress concerning (ϕ, Γ)-modules in the
“Lubin-Tate” setting. This work was motivated by the p-adic local Langlands correspondence …