Wojciech J. Gajda

Streszczenie: 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 quickly explain the linearization of the problem using generalized Serre-Tate coordinates. I will then present the role of monodromy groups of isocrystals in this context. This is a joint work with Pol van Hoften.