English

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).

Keywords

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}
}