A characteristic p analogue of the André--Pink--Zannier conjecture
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908369331159040 |
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| author | Lam, Yeuk Hay Joshua Shankar, Ananth N. |
| author_facet | Lam, Yeuk Hay Joshua Shankar, Ananth N. |
| contents | We investigate the analogue of the André--Pink--Zannier conjecture in characteristic $p$. Precisely, we prove it for ordinary function field-valued points with big monodromy, in Shimura varieties of Hodge type. We also prove an algebraic characteristic $p$ analogue of Hecke-equidistribution (as formulated by Mazur) for Shimura varieties of Hodge type. We prove our main results by a global and local analysis of prime-to-$p$ Hecke correspondences, and by showing that Weyl special points are abundant in positive characterstic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_12521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A characteristic p analogue of the André--Pink--Zannier conjecture Lam, Yeuk Hay Joshua Shankar, Ananth N. Number Theory Algebraic Geometry We investigate the analogue of the André--Pink--Zannier conjecture in characteristic $p$. Precisely, we prove it for ordinary function field-valued points with big monodromy, in Shimura varieties of Hodge type. We also prove an algebraic characteristic $p$ analogue of Hecke-equidistribution (as formulated by Mazur) for Shimura varieties of Hodge type. We prove our main results by a global and local analysis of prime-to-$p$ Hecke correspondences, and by showing that Weyl special points are abundant in positive characterstic. |
| title | A characteristic p analogue of the André--Pink--Zannier conjecture |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.12521 |