MS Seminar (Mathematics - String Theory)

Speaker: Yoichi Mieda (Kyushu U)
Title: Lefschetz trace formula and the l-adic cohomology of the Rapoport-Zink spaces
Date: Tue, Nov 16, 2010, 15:30 - 17:00
Place: Seminar Room A
Abstract: (Part 1)
The Rapoport-Zink spaces are generalizations of the Lubin-Tate space, which gives a geometric realization of the local Langlands correspondence for GL(n) and the local Jacquet-Langlands correspondence.
In the first part, I will recall what is expected for the l-adic cohomology of the Rapoport-Zink spaces.
I will also explain a method of calculating them by using Lefschetz trace formula for rigid spaces.

(Part 2)
First I will discuss on the Lefschetz trace formula for rigid spaces which are not necessarily proper over a non-archimedean field.
Next I will give the precise definition of the Rapoport-Zink space for GSp(4) and explain how our trace formula can be used to calculate the l-adic cohomology of it.
Remarks: There will be a 5-minute break after the first 25 min.