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} …

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 …

Cet article s' inscrit dans le cadre d'une hypothétique correspondance de Langlands p-
adique. Notre but est d'établir une bijection naturelle entre la famille des représentations …

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 …

We extend the $ p $-adic local Langlands correspondence for $\textbf {GL} _2 (\mathbf {Q}
_p) $ to a correspondence $\Delta\mapsto\Pi (\Delta) $ between $(\varphi,\Gamma) …

Cet article s' inscrit dans le cadre de la correspondance de Langlands locale p-adique pour
la série principale unitaire de GL2 (Qp). Nous utilisons la théorie des (ϕ, Γ)-modules de …

The p-adic local Langlands correspondence for GL_2 (Q_p) is given by an exact functor
from unitary Banach representations of GL_2 (Q_p) to representations of the absolute Galois …

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 …

If f is a modular form of weight≥ 2, the representation of GL2 (Qp) attached to it by the p-adic
local Langlands correspondence encodes the representation attached by the classical …

We construct some locally ℚ p-analytic representations of GL 2 (L), L a finite extension of ℚ
p, associated to some p-adic representations of the absolute Galois group of L. We prove …