We prove a variety of results on the existence of automorphic Galois representations lifting a residual automorphic Galois representation. We prove a result on the structure of deformation rings ofâ€¦ (More)

We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adicâ€¦ (More)

Let p > 2 be prime. We prove the weight part of Serreâ€™s conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzardâ€“Diamondâ€“Jarvis conjecture forâ€¦ (More)

We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call â€˜potential diagonalizabilityâ€™. This result allows for â€˜change of weightâ€™ andâ€¦ (More)

We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l-adic Galois representations associated to regular algebraic conjugate self-dual cuspidalâ€¦ (More)

In this note we improve on the results of our earlier paper [BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.

We prove that for forms of U(3) which are compact at infinity and split at places dividing a prime p, in generic situations the Serre weights of a mod p modular Galois representation which isâ€¦ (More)