# The image of Colmez's Montreal functor

Vytautas Paskunas

Number | 16 |
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Author | Vytautas Paškūnas |

Year | 2013 |

We prove a conjecture of Colmez concerning the reduction modulo p of invariant lattices in irreducible admissible unitary p-adic Banach space representations of GL2(Qp) with p≥5. This enables us to restate nicely the p-adic local Langlands correspondence for GL2(Qp) and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.