Hecke orbits in moduli spaces -- Frans Oort

The Zariski closure of the Hecke orbit of a point in the moduli space of abelian varieties in positive characteristic equals the related Newton polygon stratum. This was proved by Ching-Li Chai in 1995 for ordinary abelian varieties. The general case was conjectured in 1993 by FO, and recently proved by C.-L. Chai and FO. I will present a survey and one of the details of the proof.