{
  "id": "math/9803169",
  "version": "v1",
  "published": "1998-03-13T00:00:00.000Z",
  "updated": "1998-03-13T00:00:00.000Z",
  "title": "Torsion points of abelian varieties in abelian extensions",
  "authors": [
    "Wolfgang M. Ruppert"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let A be an abelian variety defined over a number field K and let Kab be the maximal abelian extension of K. We show that there only finitely many torsion points of A which are defined over Kab iff A has no abelian subvariety with complex multiplication over K. We use this to give another proof of Ribet's result that A has only finitely many torsion points which are defined over the cyclotomic extension of K.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-03-13T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "torsion points",
      "maximal abelian extension",
      "number field",
      "cyclotomic extension",
      "ribets result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......3169R"
    }
  }
}