Reduction and isogenies of elliptic curves

Mentzelos Melistas

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arXiv · 2310.15914

Reduction and isogenies of elliptic curves

Mentzelos Melistas

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Abstract

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 $\mathbb{Q}$.

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Mentzelos Melistas. 2023-10-24. Reduction and isogenies of elliptic curves. https://arxiv.org/abs/2310.15914

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