New p-adic perspectives on canonical integral models for Shimura varieties
March 2, 2026 – March 6, 2026
This workshop, sponsored by AIM and the NSF, will be devoted to new developments in integral p-adic cohomology theories, focusing in particular on their applications to the study of integral models of Shimura varieties.
The past decade has seen several innovations in p-adic cohomology, with the introduction, first of perfectoid geometry, and more recently, of prismatic cohomology and its refinements. The power of these general theories has been brought to bear on the problem of understanding the arithmetic behavior of Shimura varieties, both local and global, with applications to key number-theoretic frameworks like the Langlands and Kudla programs. The workshopâs goal is to push these applications further, and to explore new ones, with the eventual goal of obtaining a systematic and naturally functorial theory of integral models of Shimura varieties.
The main topics for the workshop are
- Prismatic/syntomic realizations for Shimura varieties beyond hyperspecial level
- Characterizing and constructing integral models of local and global Shimura varieties
- Applications to automorphic forms and cohomology of Shimura varieties
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
For more information email workshops@aimath.org