Reduction and isogenies of elliptic curves

Mentzelos Melistas

Reduction and isogenies of elliptic curves

Number Theory 2024-04-18 v2

Authors: Mentzelos Melistas

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 $\mathbb{Q}$ .

Keywords

elliptic curves isogenies discrete valuation ring kodaira reduction prime degree

Cite

@article{arxiv.2310.15914,
  title  = {Reduction and isogenies of elliptic curves},
  author = {Mentzelos Melistas},
  journal= {arXiv preprint arXiv:2310.15914},
  year   = {2024}
}

Comments

Minor changes. Final manuscript version. To appear in Acta Arithmetica

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