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Journals and Conferences
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 of… (More)
We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin.
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-adic… (More)
We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.
Let p > 2 be prime. We prove the weight part of Serre’s conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard–Diamond–Jarvis conjecture for… (More)
We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call ‘potential diagonalizability’. This result allows for ‘change of weight’ and… (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 cuspidal… (More)
We prove the Breuil–Mézard conjecture for 2-dimensional potentially Barsotti–Tate representations of the absolute Galois group GK , K a finite extension of Qp, for any p > 2 (up to the question of… (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 is… (More)