Mod $p$ points on Shimura varieties of parahoric level

Abstract: The conjecture of Langlands-Rapoport gives a conjectural description of the mod $p$ points of Shimura varieties, with applications towards computing the (semi-simple) zeta function of these Shimura varieties. The conjecture was proven by Kisin for abelian type Shimura varieties at primes of (hyperspecial) good reduction, after having constructed smooth integral models. For primes of (parahoric) bad reduction, Kisin and Pappas have constructed `good' integral models and the conjecture naturally generalises to this setting. In this talk we will discuss work in progress towards the conjecture for these integral models, under some hypotheses, building on earlier work of Zhou.

number theoryrepresentation theory

Audience: researchers in the topic

Cross Atlantic Representation Theory and Other topics ONline (CARTOON) conference