{
  "id": "1407.1099",
  "version": "v1",
  "published": "2014-07-04T00:47:12.000Z",
  "updated": "2014-07-04T00:47:12.000Z",
  "title": "Indivisibility of Heegner points in the multiplicative case",
  "authors": [
    "Christopher Skinner",
    "Wei Zhang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For certain elliptic curves $E$ over $\\mathbb{Q}$ with multiplicative reduction at a prime $p\\geq 5$, we prove the $p$-indivisibility of the derived Heegner classes defined with respect to an imaginary quadratic field $K$, as conjectured by Kolyvagin. The conditions on $E$ include that $E[p]$ be irreducible and not finite at $p$ and that $p$ split in the imaginary quadratic field $K$, along with certain $p$-indivisibility conditions on various Tamagawa factors. The proof extends the arguments of the second author for the case where $E$ has good ordinary reduction at~$p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-04T00:47:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40",
      "11G05",
      "11F67"
    ],
    "keywords": [
      "heegner points",
      "multiplicative case",
      "imaginary quadratic field",
      "ordinary reduction",
      "elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.1099S"
    }
  }
}