The image of Colmez’s Montreal functor

Paškūnas, Vytautas

Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 1-191.

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

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