Some new cases of Zilber-Pink in $Y(1)^3$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917294646493184 |
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| author | Daw, Christopher Orr, Martin Papas, Georgios |
| author_facet | Daw, Christopher Orr, Martin Papas, Georgios |
| contents | We prove the Zilber-Pink conjecture for curves in $Y(1)^3$ that intersect a modular curve in the boundary. We also give an unconditional result for unlikely intersection points having few places of supersingular reduction where they are close to a fixed base point. Both results are proved using the G-functions method for unlikely intersections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some new cases of Zilber-Pink in $Y(1)^3$ Daw, Christopher Orr, Martin Papas, Georgios Number Theory Algebraic Geometry 11G18, 11G50, 14G35, 14G22 We prove the Zilber-Pink conjecture for curves in $Y(1)^3$ that intersect a modular curve in the boundary. We also give an unconditional result for unlikely intersection points having few places of supersingular reduction where they are close to a fixed base point. Both results are proved using the G-functions method for unlikely intersections. |
| title | Some new cases of Zilber-Pink in $Y(1)^3$ |
| topic | Number Theory Algebraic Geometry 11G18, 11G50, 14G35, 14G22 |
| url | https://arxiv.org/abs/2510.09603 |