The image of Colmez’s Montreal functor
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 GL 2 (𝐐 p ) with p 5 . This enables us to restate nicely the with 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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     title = {The image of {Colmez{\textquoteright}s} {Montreal} functor},
     journal = {Publications Math\'ematiques de l'IH\'ES},
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     publisher = {Springer Berlin Heidelberg},
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Paškūnas, Vytautas. The image of Colmez’s Montreal functor. Publications Mathématiques de l'IHÉS, Tome 118 (2013), pp. 1-191. doi : 10.1007/s10240-013-0049-y. http://archive.numdam.org/articles/10.1007/s10240-013-0049-y/

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