Residual automorphic representations of Sp4

Automorphic Realization of Residual Galois Representations

The “Galois representations” of the title are modular representations ρ of the Galois groups of a number field F , and the ”automorphic realization” of the title refers to obtaining these representations as constituents of Galois representations attached to automorphic representations of general linear groups over F . The present article refines the moduli-theoretic arguments of [HST] to show t...

CUP PRODUCTS IN AUTOMORPHIC COHOMOLOGY: THE CASE OF Sp4

We study limits of discrete series with infinitesimal character zero for Sp4: their n-cohomology and their contribution to “nonclassical” automorphic cohomology of the period domain for Hodge structures of mirror quintic type. As an application, we obtain the first generalization beyond SU(2, 1) of a result of [C1], showing that this cohomology can be reached by cup products of pairs of “classi...

Introduction to Automorphic Representations

Unipotent Automorphic Representations : Conjectures

In these notes, we shall attempt to make sense of the notions of semisimple and unipotent representations in the context of automorphic forms. Our goal is to formulate some conjectures, both local and global, which were originally motivated by the trace formula. Some of these conjectures were stated less generally in lectures [2] at the University of Maryland. The present paper is an update of ...

Automorphic Representations of Adele Groups