A Lehmer-type lower bound for the canonical height on elliptic curves over function fields

Abstract

Let F be the function field of a curve over an algebraically closed field with char(F)≠2,3, and let E/F be a non-isotrivial elliptic curve. Then for all finite extensions K/F and all non-torsion points P∈E(K), the F-normalized canonical height of P is bounded below byhˆE(P)≥110500⋅hF(jE)2⋅[K:F]2.