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 GL2(Q p ) with p≥5. This enables us to restate nicely the p-adic local Langlands correspondence for GL2(Q p ) and deduce a conjecture of Breuil on irreducible admissible unitary completions of locally algebraic representations.
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Paškūnas, V. The image of Colmez’s Montreal functor. Publ.math.IHES 118, 1–191 (2013). https://doi.org/10.1007/s10240-013-0049-y
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DOI: https://doi.org/10.1007/s10240-013-0049-y