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 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 regular integral canonical models for Shimura varieties attached to Spin and
orthogonal groups at (possibly ramified) primes. Work of Vasiu–Zink then shows that the …

In this article, we prove results about the cohomology of compact unitary group Shimura
varieties at split places. In nonendoscopic cases, we are able to give a full description of the …

We study the intersections of special cycles on a unitary Shimura variety of signature (n− 1,
1) and show that the intersection multiplicities of these cycles agree with Fourier coefficients …

We construct projective toroidal compactifications for integral models of Shimura varieties of
Hodge type. We also construct integral models of the minimal (Satake-Baily-Borel) …

We construct ap-adic Eisenstein measure with values in the space of p-adic automorphic
forms on certain unitary groups. Using this measure, we p-adically interpolate certain special …

We extend the results of Kottwitz on points of Shimura varieties over finite fields to cases of
bad reduction. The “test function” whose twisted orbital integrals appear in the final …

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 …

The goal of this paper is to study certain p-adic differential operators on automorphic forms
on U (n, n). This is one step in an ongoing project to construct certain p-adic L-functions …