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arXiv · 2112.12422

On the ordinary Hecke orbit conjecture

Pol van Hoften
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Abstract

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 $p$-adic monodromy 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 results of Howe.

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Pol van Hoften. 2021-12-23. On the ordinary Hecke orbit conjecture. https://doi.org/10.2140/ant.2024.18.847

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