(G-mu)-Displays, Rapoport-Zink spaces and integral models of local Shimura varieties
Sebastian Bartling
2023-05-23 15:30-17:00
MCM110&Online
Speaker: Dr. Sebastian Bartling (University Duisburg-Essen)Time: 15:30-17:00 May 23, 2023 (Tuesday)
Place: MCM110 & Online (ZOOM ID: 332 983 6068 Password: mcm1234)
Title: (G-mu)-Displays, Rapoport-Zink spaces and integral models of local Shimura varieties
Abstract: Local Shimura varieties are group-theoretic generalizations of generic fibers of Rapoport-Zink spaces and their coverings. Thanks to the work of many people, we now also have access to (several constructions in varying degrees of generalities of) integral models of local Shimura varieties at parahoric level in the abelian type case. All these constructions reduce to the representability result of Rapoport-Zink concerning their moduli of p-divisible groups (resp. to Siegel-Shimura varieties). The general case remains for now however mysterious.
I will explain some progress towards the general hyper special case under some assumptions: (i) a work in progress concerning a new purely display-theoretic proof of the representability of Rapoport-Zink spaces and (ii) the comparison between the Bültel-Pappas approach to the construction of integral models of local Shimura-varieties using G-mu-Displays and Scholze’s approach using Shtuka and some applications of this.
