A lower bound for the canonical height on elliptic curves over abelian extensions

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67351Let 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).Number TheoryCommutative Algebra11G05 (Primary) 11G10, 14G25, 14K15 (Secondary)A lower bound for the canonical height on elliptic curves over abelian extensionstext