Formes modulaires de Hilbert modulo $p$ et valeurs d'extensions entre caractères galoisiens

• DOI: 10.24033/asens.2230
• Publication Date: 2017-03-25T16:17:11Z
• Authors: Christophe Breuil; Fred Diamond
• Keywords: [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]; Mathematics - Number Theory; 11F80 (Primary) 22E50 (Secondary); FOS: Mathematics; [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]; Number Theory (math.NT); 0101 mathematics; 01 natural sciences; [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

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.<br/>in French, to appear in Annales Scientifiques de l'Ecole Normale Superieure<br/>