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arXiv:math/0312393 [math.NT]AbstractReferencesReviewsResources

A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions

Matthew Baker, Joseph Silverman

Published 2003-12-22, updated 2004-04-12Version 2

Let A be an abelian variety defined over a number field K, and consider the canonical height function attached to a symmetric ample line bundle L on A. We prove that there is a positive lower bound C (depending on A, K, and L) for the canonical height of non-torsion points on A defined over the maximal abelian extension K^ab of K.

Comments: v2 (23 pages), to appear in Mathematical Research Letters. Revised statement and proof of Proposition 7.3, added Lemma 7.9. Some other small revisions made as well
Categories: math.NT, math.AG
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