On the ordinary Hecke orbit conjecture
| Autor: | van Hoften, Pol |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 18 (2024) 847-898 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2024.18.847 |
| Popis: | 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. Comment: 44 pages; v3 is a minorly revised version of v1; main results unchanged |
| Databáze: | arXiv |
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