Automorphic Forms and Arithmetic

We will present a new notion of isogeny between ‘p-divisible groups with additional structure’ that employs the cohomological stacks of Drinfeld and Bhatt-Lurie—-in particular the theory of apertures developed in prior work with Gardner—-and combines it with some invariant theoretic tools familiar to the geometric Langlands and representation theory community, namely the Vinberg monoid and the wonderful compactification. This gives a uniform construction of p-Hecke correspondeces and Rapoport-Zink spaces associated with unramified local Shimura data. In particular, we give the first general construction of RZ spaces associated with exceptional groups. This work is joint with Si Ying Lee.