Modul: MAT770 Oberseminar: Algebraische Geometrie

## Hecke orbits on Shimura varieties

Talk by Dr. Marco D'Addezio

**Date:** 28.11.22 **Time:** 13.15 - 14.45 **Room:** Y27H25

I will talk about the proof of the Hecke orbit conjecture for Shimura varieties of Hodge type. This is a conjecture proposed by Chai and Oort on the geometry of the reduction modulo p of Shimura varieties. After recalling the statement, I will explain how to linearise the problem using some “generalised Serre-Tate coordinates” on central leaves. Subsequently, I will explain how the monodromy groups of F-isocrystals enter into the picture. I will end the talk with some ideas on how to prove a certain local monodromy theorem, which is a crucial step in the proof of the conjecture. This is a joint work with Pol van Hoften.