{
  "id": "math/0502261",
  "version": "v1",
  "published": "2005-02-13T12:20:01.000Z",
  "updated": "2005-02-13T12:20:01.000Z",
  "title": "A refined counter-example to the support conjecture for abelian varieties",
  "authors": [
    "Michael Larsen",
    "René Schoof"
  ],
  "comment": "3 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "If A/K is an abelian variety over a number field and P and Q are rational points, the original support conjecture asserted that if the order of Q (mod p) divides the order of P (mod p) for almost all primes p of K, then Q is obtained from P by applying an endomorphism of A. This is now known to be untrue. In this note we prove that it is not even true modulo the torsion of A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-13T12:20:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10"
    ],
    "keywords": [
      "abelian variety",
      "refined counter-example",
      "number field",
      "rational points",
      "original support conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2261L"
    }
  }
}