On the ordinary Hecke orbit conjecture
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909170825953280 |
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| author | van Hoften, Pol |
| author_facet | van Hoften, Pol |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12422 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the ordinary Hecke orbit conjecture van Hoften, Pol Number Theory Algebraic Geometry Primary 11G18, Secondary 14G35 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. |
| title | On the ordinary Hecke orbit conjecture |
| topic | Number Theory Algebraic Geometry Primary 11G18, Secondary 14G35 |
| url | https://arxiv.org/abs/2112.12422 |