Relative cohomology of cuspidal forms on PEL-type Shimura varieties

Compactifications of Splitting Models of Pel-type Shimura Varieties

We construct toroidal and minimal compactifications, with expected properties concerning stratifications and formal local structures, for all integral models of PEL-type Shimura varieties defined by taking normalizations over the splitting models considered by Pappas and Rapoport. (These include, in particular, all the normal flat splitting models they considered.)

Automorphic Forms on Shimura Varieties

On the geometry and cohomology of some simple Shimura varieties

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 ...

Haruzo Hida ’ s p - adic automorphic forms on Shimura varieties

Three topics figure prominently in themodern higher arithmetic: zeta-functions, Galois representations, and automorphic forms or, equivalently, representations. The zeta-functions are attached to both the Galois representations and the automorphic representations and are the link that joins them. Although by and large abstruse and often highly technical the subject has many claims on the attent...