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 a good integral model and the conjecture was generalised to this setting by Rapoport. In this talk I will discuss recent results towards the conjecture for these integral models, under minor hypothesis, building on earlier work of Zhou. Along the way we will see irreducibility results for various stratifications on special fibers of Shimura varieties, including irreducibility of central leaves and Ekedahl-Oort strata.

algebraic geometrynumber theory

Audience: researchers in the topic

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MIT number theory seminar

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