Zilber-Pink in a product of modular curves assuming multiplicative degeneration
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913713163862016 |
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| author | Daw, Christopher Orr, Martin |
| author_facet | Daw, Christopher Orr, Martin |
| contents | We prove the Zilber--Pink conjecture for curves in $Y(1)^n$ whose Zariski closure in $(\mathbb{P}^1)^n$ passes through the point $(\infty, \ldots, \infty)$, going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following André's G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-archimedean places. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_06338 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zilber-Pink in a product of modular curves assuming multiplicative degeneration Daw, Christopher Orr, Martin Number Theory Algebraic Geometry 11G18, 11G50, 14G35 We prove the Zilber--Pink conjecture for curves in $Y(1)^n$ whose Zariski closure in $(\mathbb{P}^1)^n$ passes through the point $(\infty, \ldots, \infty)$, going beyond the asymmetry condition of Habegger and Pila. Our proof is based on a height bound following André's G-functions method. The principal novelty is that we exploit relations between evaluations of G-functions at unboundedly many non-archimedean places. |
| title | Zilber-Pink in a product of modular curves assuming multiplicative degeneration |
| topic | Number Theory Algebraic Geometry 11G18, 11G50, 14G35 |
| url | https://arxiv.org/abs/2208.06338 |