On the ordinary Hecke orbit conjecture

On the ordinary Hecke orbit conjecture Pol van HoftenWe prove the ordinary Hecke orbit conjecture for Shimura varieties of Hodge type at primes of good reduction.We make use of the global Serre-Tate coordinates of Chai as well as recent results of D'Addezio about the monodromy groups of isocrystals.The new ingredients in this paper are a general monodromy theorem for Hecke-stable subvarieties for Shimura varieties of Hodge type, and a rigidity result for the formal completions of ordinary Hecke orbits.Along the way, we show that classical Serre-Tate coordinates can be described using unipotent formal groups, generalising a result of Howe.p f ) be a sufficiently small compact open subgroup.Let Sh G be the special fibre of the canonical integral model of the Shimura variety of level K p K p at a prime v above p of E, constructed in Kisin 2010; Kim and Madapusi Pera 2016.