Date: October 27 (Sun), 2024
Place: Department of Mathematics, Kyoto University
North campus, Graduate School of Science Bldg. No.3
Lecture room 3-108
Zoom:
Zoom meeting ID: 945 9011 0248
Passcode: shimura
Speakers:
Zachary Gardner (Boston College)
Jean-Stefan Koskivirta (Saitama University)
Joseph Muller (The University of Tokyo)
Stefan Reppen (The University of Tokyo)
Program:
9:30-10:30 Zachary Gardner
10:45-11:45 Stefan Reppen
13:30-14:30 Joseph Muller
14:45-15:45 Jean-Stefan Koskivirta
Titles and abstracts (to be updated):
Zachary Gardner (Boston College)
Title: Prismatic Rapoport-Zink spaces associated to general linear groups
Abstract: By-now classical work of Rapoport-Zink shows that Rapoport-Zink spaces associated to general linear groups are represented by p-adic formal schemes which are locally formally of finite type. The approach employed by Rapoport-Zink is largely topological in nature, and relies on the so-called decency assumption and the resulting structure theory of the appropriate Bruhat-Tits building. More recently, Bartling-Hoff gave a totally new proof of the same result in the "formal" case using (truncated) Witt displays and the representability theorem of Artin. In this talk, I will explain how the methods of Bartling-Hoff can be adapted to show that prismatic Rapoport-Zink spaces associated to general linear groups are represented by derived p-adic formal schemes which are locally formally of finite type.
Jean-Stefan Koskivirta (Saitama University)
Title: Singluarities of Ekedahl-Oort strata.
Abstract: The special fiber of Shimura varieties admits several natural stratifications by locally closed subsets, whose Zariski closures can be very singular. In this talk, we investigate the singularities of Ekedahl--Oort strata using two separate methods : by relating them to the theory of canonical filtrations, and by computing the order of vanishing of generalized Hasse invariants. This is joint work in progress with Lorenzo La Porta (Padova University) and Stefan Reppen (The University of Tokyo).
Joseph Muller (The University of Tokyo)
Title: Cohomology of supersingular loci of Shimura varieties of Coxeter type
Abstract: The supersingular locus of certain Shimura varieties admits a stratification by Deligne-Luzstig varieties of Coxeter type, whose combinatorics is related to the Bruhat-Tits building of the underlying p-adic group. By computing the (l-adic) cohomology of a stratum, then looking into the spectral sequence associated to the stratification, one may expect to describe the cohomology of the supersingular locus in terms of automorphic forms. I will illustrate this idea in the case of the PEL GU(1,n-1) Shimura variety over a prime which is inert or ramified.
Stefan Reppen (The University of Tokyo)
Title: Systems of Hecke eigenvalues on subschemes of Shimura varieties
Abstract: We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod p abelian type compact Shimura variety at hyperspecial level are the same as those appearing in any Hecke-equivariant closed subscheme.
Support:
This workshop is partially supported by KAKENHI (Grants-in-Aid for Scientific Research) 24H00015 and KAKENHI (Grants-in-Aid for Scientific Research) 24K16887.
Organizers:
Kazuhiro Ito (Tohoku University), Tetsushi Ito (Kyoto University, Department of Mathematics)