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

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

2003-12-22

arxiv.org/abs/math/0312393v2

Mathematics

Number Theory

v2 (23 pages), to appear in Mathematical Research Letters. Revised statement and proof of Proposition 7.3, added Lemma 7.9. So

Scientific paper

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.

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