A new approach to isogenies and Hecke correspondences in mixedcharacteristic | BIMSA-YMSC Tsinghua Number Theory Seminar

Abstract

Recently, with Gardner and Mathew, I have constructed well-behaved stacks of prismatic (G,mu)displays, which give a "inear algebraic’ construction of p-divisible groups with additional structureThis verifies some conjectures of Drinfeld. in this talk, I'll give an impressionistic overview of theseobjects, and explain how they can be used to get a fresh understanding-in the hyperspecial case-..of Rapoport-Zink spaces (associated with arbitrary reductive aroups!). smooth intearal canonicamodels of Shimura varieties of abelian type, as well as of p-Hecke correspondences on thesespaces. In particular, one gets a 'pure thought' proof of Scholze's conjectural cartesian diagramrelating 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. Thiswork is joint with Si Ying Lee.