{
  "id": "math/0211118",
  "version": "v3",
  "published": "2002-11-06T18:11:02.000Z",
  "updated": "2003-02-28T17:35:31.000Z",
  "title": "The support problem for abelian varieties",
  "authors": [
    "Michael Larsen"
  ],
  "comment": "7 pages, plain TeX. The statements of the main theorem and main corollary are slightly weakened to coincide with what is actually proved in the paper. There are a few other minor changes. To appear in the Journal of Number Theory",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $A$ be an abelian variety over a number field $K$. If $P$ and $Q$ are $K$-rational points of $A$ such that the order of the reduction of $Q$ divides that of $P$ for all but finitely many primes of the ring of integers of $K$, then there exists a $K$-endomorphism $\\phi$ of $A$ and a positive integer $k$ such that $kQ = \\phi(P)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2003-02-28T17:35:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11R34"
    ],
    "keywords": [
      "abelian variety",
      "support problem",
      "rational points",
      "number field"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....11118L"
    }
  }
}