Towards a p-adic nowhere density conjecture of Hecke Orbits
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909642440835072 |
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| author | Fu, Yu |
| author_facet | Fu, Yu |
| contents | We propose a conjecture on the $p$-adic nowhere density of the Hecke orbit of subvarieties of Hodge type Shimura varieties. By investigating the monodromy of $p$-adic Galois representations associated with points on such Shimura varieties, we prove that the locus in a formal $\mathcal{O}_K$-neighborhood of a mod $p$ point that has large monodromy is open dense, where $K$ is a totally ramified finite extension of $\breve{\mathbb{Q}}_p.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a p-adic nowhere density conjecture of Hecke Orbits Fu, Yu Number Theory Algebraic Geometry We propose a conjecture on the $p$-adic nowhere density of the Hecke orbit of subvarieties of Hodge type Shimura varieties. By investigating the monodromy of $p$-adic Galois representations associated with points on such Shimura varieties, we prove that the locus in a formal $\mathcal{O}_K$-neighborhood of a mod $p$ point that has large monodromy is open dense, where $K$ is a totally ramified finite extension of $\breve{\mathbb{Q}}_p.$ |
| title | Towards a p-adic nowhere density conjecture of Hecke Orbits |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2506.06932 |