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 …

We construct algebras of endomorphisms in the derived category of the cohomology of
arithmetic manifolds, which are generated by Hecke operators. We construct Galois …

On any smooth algebraic variety over a $ p $-adic local field, we construct a tensor functor
from the category of de Rham $ p $-adic\'etale local systems to the category of filtered …

Lorsque le niveau en qui lui est associée. En ce qui concerne la torsion, dans un cadre bien
moins général que Caraiani et Scholze («On the generic part of the cohomology of compact …

We show that the automorphic étale cohomology of a (possibly noncompact) PEL-type or
Hodge-type Shimura variety in characteristic zero is canonically isomorphic to the …

We consider the interior cohomology (and the Hodge graded pieces in the case of the de
Rham realization) of general–not necessarily compact–PEL-type Shimura varieties with …

The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for $\mathrm {GL} _n $ over number fields from the last decade and a half. We …

We show that the compactly supported cohomology of certain. More precisely, we use the
vanishing result for Shimura varieties to eliminate the nilpotent ideal in the construction of …

The goal of these lecture notes is to survey progress on the global Langlands reciprocity
conjecture for GLn over number fields from the last decade and a half. We highlight results …

In this introductory article, we will explain what Shimura varieties are and why they are
useful, with an emphasis on examples. We will also describe various compactifications of …