| Résume | We prove many cases of a recent conjecture of Buzzard, Diamond andJarvis concerning the possible weights of mod p Hilbert modular forms.The techniques we use are an extension of a recent modularity liftingtheorem of Mark Kisin's, together with an extension of a liftingtheorem of Ramakrishna, and some computations in p-adic Hodge theorywhich amount to some cases of (a generalisation of) the Breuil-Mezardconjecture for potentially Barsotti-Tate representations of anunramified extension of Qp. |
