A new approach to canonical integral models of Shimura varieties

Abstract: Since Langlands's earliest paper on his now famous program, canonical integral models of Shimura varieties have occupied a central role in modern number theory. In this talk I will discuss how recent advances in integral $p$-adic Hodge theory allows one to make great progress in understanding these models: both in constructing new examples of such models, and greatly explicating the structure of already-existing models. No prior knowledge of advanced $p$-adic Hodge theory or Shimura varieties will be assumed, but familiarity with elliptic curves/abelian varieties and $p$-divisible groups will be very helpful.

This talk is based on joint works: one with Keerthi Madapusi, and the other with Naoki Imai and Hiroki Kato.

algebraic geometrynumber theory

Audience: researchers in the discipline

Boston University Number Theory Seminar