Аннотация:
I will talk about the proof of the
Hecke orbit conjecture for Shimura varieties in characteristic p, as
formulated by Chai and Oort. After reviewing the statement in the
case of the moduli space of abelian varieties, I will explain the
linearisation of the problem using generalised Serre-Tate
coordinates. I will then present the role of monodromy groups of
isocrystals in this context. In the end, I will explain how the
conjecture gives the surjectivity of the period map for K3
surfaces. This is a joint work with Pol van Hoften.
