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

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.

No reviews yet.

No comments yet.