Supersingular primes and Bogomolov property

2025/04/18 by Sahu, Soumyadip · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.13498

Abstract

Let E be an elliptic curve over a number field K with at least one real embedding and L be a finite extension of K. We generalize a result of Habegger to show that L(E_tor), the field generated by the torsion points of E over L, has the Bogomolov property. Moreover, the Néron-Tate height on E(L(E_tor)) also satisfies a similar discreteness property. Our main tool is a general criterion of Plessis that reduces the problem to the existence of a supersingular prime for E satisfying certain conditions.

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• Small points in radical extensions of number fields

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