Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes

Abstract

Let F be a totally real field, v an unramified place of F dividing p and rho a continuous irreducible two-dimensional mod p representation of G_F such that the restriction of rho to G_{F_v} is reducible and sufficiently generic. If rho is modular (and satisfies some weak technical assumptions), we show how to recover the corresponding extension between the two characters of G_{F_v} in terms of the action of GL_2(F_v) on the cohomology mod p.

in French, to appear in Annales Scientifiques de l'Ecole Normale Superieure

References in corpus (3)

• Deformation rings and Hecke algebras in the totally real case
• On the reduction modulo p of representations of a quaternion division algebra over a p-adic field
• Congruences betwen Hilbert modular forms: constructing ordinary lifts II

Cited by in corpus (16)

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• Diagrams in the mod $p$ cohomology of Shimura curves
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• Ihara's lemma for Shimura curves over totally real fields via patching
• Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell }+y^{2m}=z^p$
• Proof of de Smit's conjecture: a freeness criterion
• Patching and Multiplicity $2^k$ for Shimura Curves
• Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$
• On the reduction modulo p of representations of a quaternion division algebra over a p-adic field
• On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
• Lattices in the cohomology of Shimura curves
• On mod p non-abelian Lubin-Tate theory for GL_2(Q_p)
• Elliptic curves over totally real quartic fields not containing $\sqrt{5}$ are modular
• On Darmon's program for the generalized Fermat equation, I
• On the constituents of the mod $p$ cohomology of Shimura curves