Reduction and isogenies of elliptic curves

Mentzelos Melistas

doi:10.4064/aa230929-17-4

Reduction and isogenies of elliptic curves

Mentzelos Melistas

Mathematics of Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

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 ℓ. We study the possible Kodaira types of reduction that E/K can have. We also prove some related results for elliptic curves over ℚ.

Original language	English
Pages (from-to)	179-192
Number of pages	14
Journal	Acta arithmetica
Volume	215
Issue number	2
DOIs	https://doi.org/10.4064/aa230929-17-4
Publication status	Published - 19 Jun 2024

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NLA

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10.4064/aa230929-17-4

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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 ℓ. We study the possible Kodaira types of reduction that E/K can have. We also prove some related results for elliptic curves over ℚ.",

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PY - 2024/6/19

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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 ℓ. We study the possible Kodaira types of reduction that E/K can have. We also prove some related results for elliptic curves over 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 ℓ. We study the possible Kodaira types of reduction that E/K can have. We also prove some related results for elliptic curves over ℚ.

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U2 - 10.4064/aa230929-17-4

DO - 10.4064/aa230929-17-4

M3 - Article

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VL - 215

SP - 179

EP - 192

JO - Acta arithmetica

JF - Acta arithmetica

IS - 2

ER -

Reduction and isogenies of elliptic curves

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Reduction and isogenies of elliptic curves

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