Représentations modulaires de GL 2 ( Q p ) et représentations galoisiennes de dimension 2
Abstract
We prove Breuil's conjecture concerning the reduction modulo
p
of trianguline representations
V
and of the representations
Π(V)
of
GL
2
(
Q
p
)
associated to them by the
p
-adic Langlands correspondence. The main ingredient of the proof is the study of some smooth irreducible representations of
B(
Q
p
)
through models built using the theory of
(ϕ,Γ)
-modules.