Number Theory Seminar

The Langlands-Rapoport conjecture gives a description of the mod p points of suitable integral models for Shimura varieties. Such results are of use, for example, in computing the local factor of the (semi-simple) Hasse-Weil zeta function of the Shimura variety. In this talk, we show the mod p isogeny classes on the integral models of Shimura varieties with parahoric level constructed by Kisin and Pappas have the form predicted by the conjecture, when the group is residually split at p. Along the way, we verify some of the He-Rapoport axioms which allow us to deduce the non-emptiness of Newton strata for these models.