Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes
Number Theory
2017-12-13 v3
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.
Cite
@article{arxiv.1208.5367,
title = {Formes modulaires de Hilbert modulo p et valeurs d'extensions galoisiennes},
author = {Christophe Breuil and Fred Diamond},
journal= {arXiv preprint arXiv:1208.5367},
year = {2017}
}
Comments
in French, to appear in Annales Scientifiques de l'Ecole Normale Superieure