A geometric approach to the uniform boundedness of $\ell$-primary torsion points
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918298932740096 |
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| author | Ji, Zhuchao Song, Jiarui Xie, Junyi |
| author_facet | Ji, Zhuchao Song, Jiarui Xie, Junyi |
| contents | We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity.
As an application, we give a new proof of the uniform boundedness of $\ell$-primary torsion points on fibers of an abelian scheme over a smooth curve, a result originally proved by Cadoret and Tamagawa. Furthermore, our approach allows us to resolve a conjecture of Cadoret and Tamagawa without additional assumptions.
Our approach is based on the theory of Betti foliations and the arithmetic equidistribution theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15089 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A geometric approach to the uniform boundedness of $\ell$-primary torsion points Ji, Zhuchao Song, Jiarui Xie, Junyi Number Theory Algebraic Geometry 11G10 We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we give a new proof of the uniform boundedness of $\ell$-primary torsion points on fibers of an abelian scheme over a smooth curve, a result originally proved by Cadoret and Tamagawa. Furthermore, our approach allows us to resolve a conjecture of Cadoret and Tamagawa without additional assumptions. Our approach is based on the theory of Betti foliations and the arithmetic equidistribution theorem. |
| title | A geometric approach to the uniform boundedness of $\ell$-primary torsion points |
| topic | Number Theory Algebraic Geometry 11G10 |
| url | https://arxiv.org/abs/2601.15089 |