Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

We prove an automorphy lifting theorem for l-adic representations where we impose a new
condition at l, which we call" potentential diagonalizability." This result allows for" change of …

There has been a clear decline in the volume of oxygen in Earth's atmosphere over the past
20 years. Although the magnitude of this decrease appears small compared to the amount of …

We show that abelian surfaces (and consequently curves of genus 2) over totally real fields
are potentially modular. As a consequence, we obtain the expected meromorphic …

We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate
representations of the absolute Galois group (up to the question of determining precise …

Using the overconvergent cohomology modules introduced by Ash–Stevens, we construct
eigenvarieties associated with reductive groups and establish some basic geometric …

A few years ago the first-named author proposed a working definition of a family of
automorphic L-functions. Then the work by the second and third-named authors on the Sato …

We prove the vanishing of the geometric Bloch–Kato Selmer group for the adjoint
representation of a Galois representation associated to regular algebraic polarized cuspidal …

We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois
representations associated to automorphic representations on rank two unitary groups for …

In this paper we give the Langlands' parameters of Langlands' packets of discrete series
using the twisted endoscopy as explained by Arthur; this holds for orthogonal, symplectic …