2024 Program for Women+ and Mathematics

Shimura varieties are an important geometric object in the Langlands program, because the Hecke (adelic group) action allows us to view various cohomology groups as Hecke modules. Moreover, the cohomology admits an integral structure when the Shimura variety has an integral model, and we hence want to extend this Hecke action integrally. I will talk about constructing integral models for Hecke correspondences in both the global and local (Rapoport-Zink spaces) setting, to get quasi-smooth derived (formal) schemes. This is joint work in progress with Keerthi Madapusi.