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Représentations modulaires de $\mathrm{GL}_2(\mathbf{Q}_p)$ et représentations galoisiennes de dimension 2

Laurent Berger
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Abstract

We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $Π(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence. The main ingredient of the proof is the study of some smooth irreducible representations of $\mathrm{B}(\mathbf{Q}_p)$ through models built using the theory of $(ϕ,Γ)$-modules.

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BibTeXRIS

Laurent Berger. 2005-10-05. Représentations modulaires de $\mathrm{GL}_2(\mathbf{Q}_p)$ et représentations galoisiennes de dimension 2. https://arxiv.org/abs/math/0510090

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