The image of Colmez's Montreal functor

Details The image of Colmez's Montreal functor The image of Colmez's Montreal functor

2010-05-12

arxiv.org/abs/1005.2008v1

Mathematics

Representation Theory

Habilitation thesis, 197 pages

Scientific paper

We prove a conjecture of Colmez concerning the reduction modulo $p$ of invariant lattices in irreducible admissible unitary $p$-adic Banach space representations of $GL_2(Q_p)$ with $p\ge 5$. This enables us to restate nicely the $p$-adic local Langlands correspondence for $GL_2(Q_p)$ and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.

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