Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions

2025/11/24 by Jenvrin, Jonathan
#11G05 #11G50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2511.19712

Abstract

We establish an explicit lower bound for the Néron-Tate height on elliptic curves with complex multiplication, for nontorsion points defined over the maximal abelian extension of a number field. Building on a strategy developed by Amoroso, David, and Zannier, we provide an alternative proof of a theorem originally due to Baker. The novelty in our approach is that it produces a lower bound that is fully explicit and independent of the discriminant of the base field.

Citations

• A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions
• Lower bounds for the canonical height on elliptic curves over abelian extensions

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