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Number Theory Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2022/05/11
17:00-18:00 Hybrid
Joseph Muller (University of Tokyo)
Cohomology of the unramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$ (ENGLISH)
Joseph Muller (University of Tokyo)
Cohomology of the unramified PEL unitary Rapoport-Zink space of signature $(1,n-1)$ (ENGLISH)
[ Abstract ]
Rapoport-Zink (RZ) spaces are moduli spaces which classify the deformations of a $p$-divisible group with additional structures. It is equipped with compatible actions of $p$-adic and Galois groups, and their cohomology is believed to play a role in the local Langlands program. So far, the cohomology of RZ spaces is entirely known only in the cases of the Lubin-Tate tower and of the Drinfeld space ; in particular both of them are RZ spaces of EL type. In this talk, we consider the unramified PEL unitary RZ space with signature $(1,n-1)$. In 2011, Vollaard and Wedhorn proved that it is stratified by generalized Deligne-Lusztig varieties, whose incidence relations mimic the combinatorics of the Bruhat-Tits building of a unitary group. We compute the cohomology of these strata and we draw some consequences on the cohomology of the RZ space. When $n = 3, 4$ we deduce
an automorphic description of the cohomology of the basic stratum in the corresponding Shimura variety via p-adic uniformization.
Rapoport-Zink (RZ) spaces are moduli spaces which classify the deformations of a $p$-divisible group with additional structures. It is equipped with compatible actions of $p$-adic and Galois groups, and their cohomology is believed to play a role in the local Langlands program. So far, the cohomology of RZ spaces is entirely known only in the cases of the Lubin-Tate tower and of the Drinfeld space ; in particular both of them are RZ spaces of EL type. In this talk, we consider the unramified PEL unitary RZ space with signature $(1,n-1)$. In 2011, Vollaard and Wedhorn proved that it is stratified by generalized Deligne-Lusztig varieties, whose incidence relations mimic the combinatorics of the Bruhat-Tits building of a unitary group. We compute the cohomology of these strata and we draw some consequences on the cohomology of the RZ space. When $n = 3, 4$ we deduce
an automorphic description of the cohomology of the basic stratum in the corresponding Shimura variety via p-adic uniformization.
