A lower bound for the canonical height on abelian varieties over abelian extensions

Let~$A$ be an abelian variety defined over a number field~$K$ and let~$\hhat$ be the canonical height function on~$A({\bar K})$ attached to a symmetric ample line bundle~$\Lcal$. We prove that there exists a constant~$C = C(A, K,{\mathcal L}) > 0$ such that~${\hat h}(P) \geq C$ for all nontorsion points~$P \in A(K^\ab)$, where~$K^\ab$ is the maximal abelian extension of~$K$.

Full Text (PDF format)

Published 1 January 2004