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A new approach to isogenies and Hecke correspondences in mixed characteristic

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

Keerthi Madapusi

时间

2024年05月20日 10:00 至 11:00

地点

Shuangqing-B627

摘要

Recently, with Gardner and Mathew, I have constructed well-behaved stacks of prismatic (G,mu)-displays, which give a 'linear algebraic' construction of p-divisible groups with additional structure. This verifies some conjectures of Drinfeld. In this talk, I'll give an impressionistic overview of these objects, and explain how they can be used to get a fresh understanding---in the hyperspecial case---of Rapoport-Zink spaces (associated with arbitrary reductive groups!), smooth integral canonical models of Shimura varieties of abelian type, as well as of p-Hecke correspondences on these spaces. In particular, one gets a 'pure thought' proof of Scholze's conjectural cartesian diagram relating Shimura varieties and spaces of shtukas on the level of p-adic formal schemes. Strikingly, one can do almost all of this without ever mentioning abelian varieties or p-divisible groups. This work is joint with Si Ying Lee.