We 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.

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关于普通赫克轨道猜想

我们证明了 Hodge 型 Shimura 簇在良好约化素数处的普通 Hecke 轨道猜想。我们利用 Chai 的全球 Serre-Tate 坐标以及 D'Addezio 关于等晶单峰群的最新结果。本文的新成分是 Hodge 型 Shimura 簇的 Hecke 稳定子簇的一般单向定理，以及普通 Hecke 轨道的形式完成的刚性结果。在此过程中，我们证明经典的塞尔-塔特坐标可以使用单能形式群来描述，概括了豪的结果。