{
  "id": "math/0312393",
  "version": "v2",
  "published": "2003-12-22T18:36:13.000Z",
  "updated": "2004-04-12T19:12:20.000Z",
  "title": "A Lower Bound for the Canonical Height on Abelian Varieties over Abelian Extensions",
  "authors": [
    "Matthew Baker",
    "Joseph Silverman"
  ],
  "comment": "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"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-12T19:12:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian variety",
      "symmetric ample line bundle",
      "maximal abelian extension",
      "non-torsion points",
      "positive lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12393B"
    }
  }
}