Reduction and isogenies of elliptic curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929316146708480 |
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| author | Melistas, Mentzelos |
| author_facet | Melistas, Mentzelos |
| contents | Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p>0$. Let $E/K$ be an elliptic curve with a $K$-rational isogeny of prime degree $\ell$. In this article, we study the possible Kodaira types of reduction that $E/K$ can have. We also prove some related results for elliptic curves over $\mathbb{Q}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15914 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Reduction and isogenies of elliptic curves Melistas, Mentzelos Number Theory Let $R$ be a complete discrete valuation ring with fraction field $K$ and perfect residue field $k$ of characteristic $p>0$. Let $E/K$ be an elliptic curve with a $K$-rational isogeny of prime degree $\ell$. In this article, we study the possible Kodaira types of reduction that $E/K$ can have. We also prove some related results for elliptic curves over $\mathbb{Q}$. |
| title | Reduction and isogenies of elliptic curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2310.15914 |