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 …

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 …

Using explicit identifications between algebraic and analytic theta functions, we compare the
algebraic constructions of toroidal compactifications by Faltings–Chai and the author, with …

Let $ F $ be a totally real field in which $ p $ is unramified. We prove that, if a cuspidal
overconvergent Hilbert cuspidal form has small slopes under $ U_p $-operators, then it is …

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 study several kinds of subschemes of mixed characteristic models of Shimura varieties
which admit good (partial) toroidal and minimal compactifications, with familiar boundary …

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 …

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 …

Shimura developed his theory of nearly holomorphic forms in his study on the algebraicity of
special L-values and Klingen Eisenstein series [42, 45]. With the goal of combining this …