EVENT DETAILS AND ABSTRACT

Title: Endoscopy and the l-adic cohomology of the Rapoport-Zink space for GSp(4)
Speaker: Tetsushi Ito
Speaker Info: Kyoto
Brief Description:
Special Note:
Abstract:

It is widely believed that the l-adic cohomology of Rapoport-Zink spaces realize the local Langlands and Jacquet-Langlands correspondences. For the Lubin-Tate spaces (i.e. for GL(n)), it was established by Harris-Taylor as an alternating sum. Boyer calculated the cohomology in each degree. In this talk, we consider supercuspidal representations in the cohomology of the Rapoport-Zink space for GSp(4) in each degree. A new phenomenon is that certain supercuspidal representations, which are related to non-tempered endoscopy (i.e. Saito-Kurokawa lifting), contribute to the cohomology outside the middle degree. The structure of local A-packets seems to reflect the cohomological degree. We propose a precise conjecture about this phenomenon, and prove it assuming Arthur's conjecture. Similar (unconditional) results are obtained also for GU(3). This is a joint work with Yoichi Mieda (Kyoto Univ).