A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions
Number Theory
2007-05-23 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0312393,
title = {A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions},
author = {Matthew Baker and Joseph Silverman},
journal= {arXiv preprint arXiv:math/0312393},
year = {2007}
}
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