Une interprétation modulaire de la variété trianguline

Abstract

Using a patching module constructed in recent work of Caraiani, Emerton, Gee, Geraghty, Pa{š}k{ū}nas and Shin we construct some kind of analogue of an eigenvariety. We can show that this patched eigenvariety agrees with a union of irreducible components of a space of trianguline Galois representations. Building on this we discuss the relation with the modularity conjectures for the crystalline case, a conjecture of Breuil on the locally analytic socle of representations occurring in completed cohomology and with a conjecture of Bellaïche and Chenevier on the complete local ring at certain points of eigenvarieties.

in French

References in corpus (2)

• On the automorphy of $l$-adic Galois representations with small residual image
• Locally analytic vectors in representations of locally p-adic analytic groups

Cited by in corpus (15)

• Deformations of polarized automorphic Galois representations and adjoint Selmer groups
• Extended eigenvarieties for overconvergent cohomology
• A local model for the trianguline variety and applications
• On the modularity of 2-adic potentially semi-stable deformation rings
• Deformation theory of the trivial mod $p$ Galois representation for ${\mathrm{GL}}_n$
• Density of automorphic points in deformation rings of polarized global Galois representations
• An adjunction formula for the Emerton-Jacquet functor
• Smoothness of definite unitary eigenvarieties at critical points
• Smoothness and Classicality on eigenvarieties
• Companion points and locally analytic socle for ${\mathrm{GL}}_2(L)$
• A derived construction of eigenvarieties
• Simple $\mathcal{L}$-invariants for ${\mathrm{GL}}_n$
• Some results on locally analytic socle for ${\mathrm{GL}}_n({\mathbb{Q}}_p)$
• Trianguline lifts of global mod $p$ Galois representations
• A note on critical $p$-adic $L$-functions