2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69669Let 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.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 wellNumber TheoryAlgebraic Geometrytext