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 $\mathrm{char}\left(F\right)\ne 2,3$, and let $E/F$ be a non-isotrivial elliptic curve. Then for all finite extensions $K/F$ and all non-torsion points $P\in E\left(K\right)$, the $F$-normalized canonical height of P is bounded below by${\hat{h}}_E\left(P\right)\ge \frac{1}{10500\cdot h_F{\left(j_E\right)}^2\cdot {[K:F]}^2}.$