Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions
Number Theory
2025-12-18 v2 Algebraic Geometry
Abstract
We establish an explicit lower bound for the N\'eron-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.
Cite
@article{arxiv.2511.19712,
title = {Explicit Uniform Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions},
author = {Jonathan Jenvrin},
journal= {arXiv preprint arXiv:2511.19712},
year = {2025}
}
Comments
12 pages Minor revisions following remarks on some imprecisions, leading to a change in the bound of the main theorem