The image of Colmez's Montreal functor

Abstract

We prove a conjecture of Colmez concerning the reduction modulo $p$ of invariant lattices in irreducible admissible unitary $p$-adic Banach space representations of $G{L}_2(Q_p)$ with $p\ge 5$. This enables us to restate nicely the $p$-adic local Langlands correspondence for $G{L}_2(Q_p)$ and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.

Proof of Prop. 5.16 modified

References in corpus (2)

• Coefficient systems and supersingular representations of $G{L}_2(F)$
• Blocks for mod $p$ representations of $G{L}_2(Q_p)$

Cited by in corpus (6)

• The Bernstein center of the category of smooth $W(k)[G{L}_n(F)]$-modules
• Théorie de Lubin-Tate non abélienne l-entière
• The universal family of semi-stable p-adic Galois representations
• Exactness of the reduction on étale modules
• A classification of the irreducible mod-p representations of U(1,1)(Q_p^2/Q_p)
• Hecke modules and supersingular representations of U(2,1)