The main result of this paper is the existence of Galois representations associated with the
mod p (or mod pm) cohomology of the locally symmetric spaces for GLn over a totally real or …

Let F be a CM number field. We prove modularity lifting theorems for regular n-dimensional
Galois representations over F without any self-duality condition. We deduce that all elliptic …

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 new modularity lifting theorems for p-adic Galois representations in situations
where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of …

We construct group-theoretical generalizations of the Hasse invariant on strata closures of
the stacks G-Zip\nolimits^ μ G-Zip μ. Restricting to zip data of Hodge type, we obtain a group …

In this paper, we establish the modularity of every elliptic curve $ E/F $, where $ F $ runs
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …

We prove that the generic part of the mod l cohomology of Shimura varieties associated to
quasi-split unitary groups of even dimension is concentrated above the middle degree …

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

In this paper we generalize the work of Harris–Soudry–Taylor and construct the compatible
systems of two-dimensional Galois representations attached to cuspidal automorphic …

We introduce a method for producing congruences between Hecke eigenclasses, possibly
torsion, in the coherent cohomology of automorphic vector bundles on certain good …