Research output: Working paper › Preprint › Academic
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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 $\mathbb{Q}$.
title = "Reduction and isogenies of elliptic curves",
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 $\mathbb{Q}$.",
Research output: Working paper › Preprint › Academic
TY - UNPB
T1 - Reduction and isogenies of elliptic curves
AU - Melistas, Mentzelos
N1 - Preprint. Submitted for publication
PY - 2023/10/24
Y1 - 2023/10/24
N2 - 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 $\mathbb{Q}$.
AB - 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 $\mathbb{Q}$.