Mathematical Research Letters

Volume 11 (2004)

Number 3

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

Pages: 377 – 396

DOI: http://dx.doi.org/10.4310/MRL.2004.v11.n3.a10

Authors

Matthew H. Baker (University of Georgia)

Joseph H. Silverman (Brown University)

Abstract

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~$K$.

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