Hyperbolicity, automorphic forms and Siegel modular varieties

Dual Bgg Complexes for Automorphic Bundles

We generalize the construction of dual BGG complexes in Faltings–Chai and Mokrane–Tilouine–Polo (from the case of Siegel modular varieties) to all smooth integral models of PEL-type Shimura varieties.

Irreducibility Criteria for Local and Global Representations

It is proved that certain types of modular cusp forms generate irreducible automorphic representations of the underlying algebraic group. Analogous Archimedean and non-Archimedean local statements are also given. Introduction One of the motivations for this paper was to show that full level cuspidal Siegel eigenforms generate irreducible, automorphic representations of the adelic symplectic sim...

On the Compactification of Arithmetically Defined Quotients of Bounded Symmetric Domains

In previous papers [13], [2], [16], [3], [ l l ] , the theory of automorphic functions for some classical discontinuous groups F, such as the Siegel or Hilbert-Siegel modular groups, acting on certain bounded symmetric domains X, has been developed through the construction of a natural compactification of X/T , which is a normal analytic space, projectively embeddable by means of automorphic fo...

AUTOMORPHIC SYMBOLS, p-ADIC L-FUNCTIONS AND ORDINARY COHOMOLOGY OF HILBERT MODULAR VARIETIES

We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general p-adic L-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the p-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ideal of the Hecke algebra. We also show its freen...

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