Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914205046669312 |
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| author | Jenvrin, Jonathan |
| author_facet | Jenvrin, Jonathan |
| contents | We establish an explicit lower bound for the Néron-Tate height on elliptic curves with complex multiplication, for nontorsion points defined over the maximal abelian extension of a number field. Building on a strategy developed by Amoroso, David, and Zannier, we provide an alternative proof of a theorem originally due to Baker. The novelty in our approach is that it produces a lower bound that is fully explicit and independent of the discriminant of the base field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions Jenvrin, Jonathan Number Theory Algebraic Geometry 11G50, 11G05 We establish an explicit lower bound for the Néron-Tate height on elliptic curves with complex multiplication, for nontorsion points defined over the maximal abelian extension of a number field. Building on a strategy developed by Amoroso, David, and Zannier, we provide an alternative proof of a theorem originally due to Baker. The novelty in our approach is that it produces a lower bound that is fully explicit and independent of the discriminant of the base field. |
| title | Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions |
| topic | Number Theory Algebraic Geometry 11G50, 11G05 |
| url | https://arxiv.org/abs/2511.19712 |