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 …

We prove new potential modularity theorems for n-dimensional essentially self-dual l-adic
representations of the absolute Galois group of a totally real eld. Most notably, in the …

The goal of this paper is to show that the cohomology of compact unitary Shimura varieties is
concentrated in the middle degree and torsion-free, after localizing at a maximal ideal of the …

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 …

Our aim is to establish some new cases of the global Langlands correspondence for GLm.
Along the way we obtain a new result on the description of the cohomology of some compact …

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 …

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 …

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 …

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 …

We generalize results of Clozel, Harris and Taylor by proving modularity lifting theorems for
ordinary l-adic Galois representations of any dimension of an imaginary CM or totally real …