EVENT DETAILS AND ABSTRACT

Title: Certain unitary Shimura varieties
Speaker: Elena Mantovan
Speaker Info: Harvard University
Brief Description:
Special Note:
Abstract:

Some conjectures of Langlands predict a correspondence between Galois representations and automorphic representations. There are "global" conjectures concerning number fields and "local" conjectures concerning p-adic fields. Moreover, for any given number field the global correspondence should be compatible with the local correspondences over its completions. In some cases, one can hope to realize the global correspondence in the cohomology of Shimura varieties and the local correspondence in the cohomology of Rapoport-Zink spaces. We will discuss a formula which describes the l-adic cohomology of a certain class of unitary Shimura varieties in terms of the cohomologies of the corresponding Igusa varieties and Rapoport-Zink spaces. This formula is obtained via the study of the geometry of the reductions in positive characteristic of these Shimura varieties. The techniques combine the approach of Harris and Taylor in their proof of the local Langlands conjecture for GL(n) and the approach of Rapoport and Zink in their construction of a p-adic uniformization of the Shimura varieties.