Supersingular primes and Bogomolov property
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910914001764352 |
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| author | Sahu, Soumyadip |
| author_facet | Sahu, Soumyadip |
| contents | Let $E$ be an elliptic curve over a number field $K$ with at least one real embedding and $L$ be a finite extension of $K$. We generalize a result of Habegger to show that $L(E_{\text{tor}})$, the field generated by the torsion points of $E$ over $L$, has the Bogomolov property. Moreover, the Néron-Tate height on $E\big(L(E_{\text{tor}})\big)$ also satisfies a similar discreteness property. Our main tool is a general criterion of Plessis that reduces the problem to the existence of a supersingular prime for $E$ satisfying certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supersingular primes and Bogomolov property Sahu, Soumyadip Number Theory Let $E$ be an elliptic curve over a number field $K$ with at least one real embedding and $L$ be a finite extension of $K$. We generalize a result of Habegger to show that $L(E_{\text{tor}})$, the field generated by the torsion points of $E$ over $L$, has the Bogomolov property. Moreover, the Néron-Tate height on $E\big(L(E_{\text{tor}})\big)$ also satisfies a similar discreteness property. Our main tool is a general criterion of Plessis that reduces the problem to the existence of a supersingular prime for $E$ satisfying certain conditions. |
| title | Supersingular primes and Bogomolov property |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.13498 |