Quantitativity on the number of rational points in the Mordell conjecture
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918318926987264 |
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| author | Yu, Jiawei Yuan, Xinyi Zhou, Shengxuan |
| author_facet | Yu, Jiawei Yuan, Xinyi Zhou, Shengxuan |
| contents | In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and proved by Vojta, Dimitrov-Gao-Habegger, and Kühne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitativity on the number of rational points in the Mordell conjecture Yu, Jiawei Yuan, Xinyi Zhou, Shengxuan Number Theory Algebraic Geometry Differential Geometry In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constants in the uniform Mordell conjecture proposed by Mazur and proved by Vojta, Dimitrov-Gao-Habegger, and Kühne. The main body of this paper consists of two parts: Part I for arithmetic estimates and Part II for analytic estimates. |
| title | Quantitativity on the number of rational points in the Mordell conjecture |
| topic | Number Theory Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2602.01820 |