We construct the compatible system of l-adic representations associated to a regular
algebraic cuspidal automorphic representation of GL_n GL n over a CM (or totally real) field …

Let F be a totally real field, K/F a totally imaginary quadratic extension, d=[F: Q], c∈ Gal (K/F)
the non-trivial Galois automorphism. Let n be a positive integer and G= Gn be the algebraic …

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 …

In this thesis, we study the compatibility between local and global Langlands
correspondences for GL n. This generalizes the compatibility between local and global class …

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 …

A GEOMETRIC PERSPECTIVE ON THE BREUIL–MÉZARD CONJECTURE Page 1 J. Inst. Math.
Jussieu (2014) 13(1), 183–223 183 doi:10.1017/S147474801300011X c Cambridge University …

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

We strengthen the compatibility between local and global Langlands correspondences for
GL n when n is even and l= p. Let L be a CM field and Π a cuspidal automorphic …

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 …

We prove the compatibility of local and global Langlands correspondences
for\(\operatorname {GL} _n\) up to semisimplification for the Galois representations …