WORKSHOP — New p-adic perspectives on canonical integral models for Shimura varieties

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 workshop’s 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.