Supercuspidal representations in l-adic cohomology of the Rapoport-Zink tower for GSp(4)


Yoichi Mieda

11:30:00 - 12:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Rapoport-Zink spaces are certain moduli spaces of quasi- isogenies of p-divisible groups with additional structures and can be regarded as p-adic analogues of Shimura varieties. Each Rapoport-Zink space has a natural system of rigid analytic coverings, which is called the Rapoport-Zink tower. A classical example is the Lubin-Tate tower, which is the Rapoport-Zink tower of GL(n). In this case, it is known that every supercuspidal representation of GL(n,Q_p) appears in the (n-1)-th l-adic cohomology of the Lubin-Tate tower. Then, we can ask the following natural problem: which kind of supercuspidal representations appear in the i-th cohomology of the Rapoport-Zink tower for GSp(4,Q_p) for each i? In this talk, we will give a partial answer to this problem. This is a joint work with Tetsushi Ito.