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Heike Harenbrock

Mittagsseminar zur Arithmetik: Hiroki Kato (MPIM Bonn): The prismatic realization for Shimura varieties of abelian type

Tuesday, 06.06.2023 10:15 im Raum SRZ 216/217

Mathematik und Informatik

On a Shimura variety, which is by definition associated to a reductive group $G$ together with some other data, there is a canonical pro-étale torsor parametrizing level structures. When the Shimura variety is of abelian type, it can be thought of as the étale realization of the ?universal motive with $G$-structure? under the guiding principle that those Shimura varieties should be moduli spaces of certain motives with $G$-structure. When the level is hyperspecial at a prime p, a crystalline realization has been constructed, by Lovering, on the p-adic completion of the integral canonical model, which corresponds to the étale realization via the p-adic Hodge theory. Given recent progress of p-adic Hodge theory, especially that of prismatic cohomology theory, it is natural to expect that Shimura varieties of abelian type admit a prismatic realization that specializes to the étale and crystalline realizations. I will talk about construction of such a realization and some consequences (joint work with Naoki Imai and Alex Youcis).



Angelegt am Monday, 05.06.2023 09:10 von Heike Harenbrock
Geändert am Monday, 05.06.2023 09:10 von Heike Harenbrock
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