A lower bound for the canonical height on elliptic curves over abelian extensions
Number Theory
2007-05-23 v1 Commutative Algebra
Abstract
Let E/K be an ellptic curve defined over a number field, let h be the canonical height on E, and let K^ab be the maximal abelian extension of K. Extending work of M. Baker, we prove that there is a positive constant C(E/K) so that every nontorsion point P in E(K^ab) satisfies h(P) > C(E/K).
Cite
@article{arxiv.math/0305041,
title = {A lower bound for the canonical height on elliptic curves over abelian extensions},
author = {Joseph H. Silverman},
journal= {arXiv preprint arXiv:math/0305041},
year = {2007}
}