Effective Mordell for curves with enough automorphisms
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908339605078016 |
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| author | Garcia-Fritz, Natalia Pasten, Hector |
| author_facet | Garcia-Fritz, Natalia Pasten, Hector |
| contents | We prove a completely explicit and effective upper bound for the Néron--Tate height of rational points of curves of genus at least $2$ over number fields, provided that they have enough automorphisms with respect to the Mordell--Weil rank of their jacobian. Our arguments build on Arakelov theory for arithmetic surfaces. Our bounds are practical, and we illustrate this by explicitly computing the rational points of a certain genus $2$ curve whose jacobian has Mordell--Weil rank $2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_10443 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective Mordell for curves with enough automorphisms Garcia-Fritz, Natalia Pasten, Hector Number Theory Primary: 14G05, Secondary: 14G40, 11G50 We prove a completely explicit and effective upper bound for the Néron--Tate height of rational points of curves of genus at least $2$ over number fields, provided that they have enough automorphisms with respect to the Mordell--Weil rank of their jacobian. Our arguments build on Arakelov theory for arithmetic surfaces. Our bounds are practical, and we illustrate this by explicitly computing the rational points of a certain genus $2$ curve whose jacobian has Mordell--Weil rank $2$. |
| title | Effective Mordell for curves with enough automorphisms |
| topic | Number Theory Primary: 14G05, Secondary: 14G40, 11G50 |
| url | https://arxiv.org/abs/2503.10443 |