Number Theory

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:

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).
Date: Monday, May 14, 2012
Time: 4:00PM
Where: Lunt 107
Contact Person: Simon Marshall
Contact email: slm@math.northwestern.edu
Contact Phone: 847-467-0715
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