arXiv math/05100902005-10-05math.NTmath.RT

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

Laurent Berger

备注：: 19 pages
发表信息：: Asterisque 330 (2010), 265--281.

英文摘要：

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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