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

摘要

Let E/K be an elliptic curve defined over a number field, let h-circumflex be the canonical height on E, and let K~(ab)/K be the maximal abelian extension of K. Extending work of M. Baker (IMRN 29 (2003) 1571–1582), we prove that there is a constant C(E/K) > 0 so that every nontorsion point PE(Kab) satisfies h-circumflex(P) > C(E/K).