# Oberseminar July 8, 2021 - Pol van Hoften

## Mod $p$ points on Shimura varieties of parahoric level

*Abstract.* The aim of this talk is to explain the conjecture of Langlands and Rapoport, which gives a conjectural description of the mod $p$ points of Shimura varieties, and to discuss some of my own work towards this conjecture at primes of (parahoric) bad reduction. I will try to keep things somewhat concrete by using the moduli space of principally polarised abelian varieties as a main example. Along the way, I will introduce the Kottwitz-Rapoport and Ekedahl-Oort stratifications on special fibers of Shimura varieties, and discuss irreducibility results for them which generalise results of Görtz-Yu and Ekedahl-van der Geer.