Abstract:

I will explain that the cohomology of a (general) Shimura variety with coefficients in automorphic etale local systems is de Rham with Hodge-Tate weights computable using relative Lie algebra cohomology, and that the same is true for the cohomology with compact support and the interior cohomology, and hence also for the intersection cohomology when the automorphic local systems are attached to algebraic representations of regular highest weights.  (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu.)