{
  "id": "1411.6352",
  "version": "v1",
  "published": "2014-11-24T05:37:16.000Z",
  "updated": "2014-11-24T05:37:16.000Z",
  "title": "Iwasawa Main Conjecture for Supersingular Elliptic Curves",
  "authors": [
    "Xin Wan"
  ],
  "comment": "15 pages, comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we prove the $\\pm$-main conjecture formulated by Kobayashi for elliptic curves with good supersingular reduction at $p$ such that $a_p=0$, using a completely new idea of reducing it to another Iwasawa-Greenberg main conjecture which is more accessible. We also prove as a corollary the refined BSD formula in the supersingular case when the analytic rank is $0$. The argument uses in an essential way the recent study on explicit reciprocity law for Beilinson-Flach elements by Kings-Loeffler-Zerbes. (This work is in progress and hopefully will appear soon).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-24T05:37:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersingular elliptic curves",
      "iwasawa main conjecture",
      "iwasawa-greenberg main conjecture",
      "explicit reciprocity law",
      "refined bsd formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.6352W"
    }
  }
}