Lehmer's conjecture for abelian varieties

Let $A$ be an abelian variety defined over a number field $K$, and let $\mathcal{L}$ be a symmetric ample line bundle on $A$. For a point $P\in A(\overline{K})$, let $D=[K(P):K]$ and let $g_0(P)$ be the dimension of the smallest algebraic subgroup of $A$ containing $P$. Lehmer's conjecture. There is a constant $C>0$ such that

$$\hat{h}_{\mathcal{L}}(P)\geq C D^{-1/g_0(P)}$$

for all non-torsion points $P\in A(\overline{K})$. This is a Lehmer-type lower bound for canonical heights on abelian varieties; the paper presents it as a conjectural application of its lower-bound results, and its resolution is not established in the supplied context.