The weights of mod p Hilbert modular forms
(Un exposé de Toby Gee au séminaire de
théorie des nombres de Chevaleret le 14 novembre 2005)
Résumé :
We prove many cases of a recent conjecture of Buzzard, Diamond and
Jarvis concerning the possible weights of mod p Hilbert modular forms.
The techniques we use are an extension of a recent modularity lifting
theorem of Mark Kisin's, together with an extension of a lifting
theorem of Ramakrishna, and some computations in p-adic Hodge theory
which amount to some cases of (a generalisation of) the Breuil-Mezard
conjecture for potentially Barsotti-Tate representations of an
unramified extension of Qp.