Automorphic Forms on Shimura Varieties

Introduction to Shimura Varieties

This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms.

Week 2: Betti Cohomology of Shimura Varieties — the Matsushima Formula

Rough exposition of the goal of this course. Hecke actions on Shimura varieties and their cohomology groups. The Matsushima formula in the classical setting; relative Lie algebra cohomology, spectral decomposition on L(Γ\G). The Matsushima formula in the adelic setting — automorphic representations appear in the Betti cohomology of Shimura varieties. Admissible (g, U)-modules and cohomological ...

Arithmeticity in the theory of automorphic forms, by Goro Shimura, Mathematical

This book is a companion to the author’s previous book [11], Euler products and Eisenstein series, published by the AMS. The books’ ultimate objective is to prove algebraicity of the critical values of the zeta functions of automorphic forms on unitary and symplectic groups. In the course of the study of the zeta functions, many important results, which were obtained by the author during 1960-2...

Shimura varieties and the Selberg trace formula

This paper is a report on work in progress rather than a description of theorems which have attained their final form. The results I shall describe are part of an attempt to continue to higher dimensions the study of the relation between the Hasse-Weil zeta-functions of Shimura varieties and the Euler products associated to automorphic forms, which was initiated by Eichler, and extensively deve...

Research Statement Modular Forms and Cycles in Locally Symmetric Spaces and Shimura Varieties: Interplay between Automorphic Forms, Representation Theory, and Arithmetic and Differential Geometry