Reduction and isogenies of elliptic curves

2023/10/24 by Melistas, Mentzelos
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.15914

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. 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 ℚ.

Related

• On the Kodaira types of elliptic curves with potentially good supersingular reduction
• On the p-isogenies of elliptic curves with multiplicative reduction over quadratic fields
• Counting elliptic curves with bad reduction over a prescribed set of primes
• Local invariants of isogenous elliptic curves
• New isogenies of elliptic curves over number fields