{
  "id": "1103.1125",
  "version": "v4",
  "published": "2011-03-06T13:29:12.000Z",
  "updated": "2011-04-20T07:57:33.000Z",
  "title": "On the classical main conjecture for imaginary quadratic fields",
  "authors": [
    "Stéphane Viguié"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let p be a prime number which is split in an imaginary quadratic field k. Let \\mathfrak{p} be a place of k above p. Let k_\\infty be the unique Z_p-extension of k which unramified outside of \\mathfrak{p}, and let K_\\intfy be a finite extension of k_\\infty, abelian over k. In case p \\notin {2,3}, we prove that the characteristic ideal of the projective limit of global units modulo elliptic units coincides with the characteristic ideal of the projective limit of the p-class groups. Our approach uses Euler systems, which were first used in this context by K.Rubin. If p \\in {2,3}, we obtain a divisibility relation, up to a certain constant.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-04-20T07:57:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G16",
      "11R23",
      "11R65"
    ],
    "keywords": [
      "imaginary quadratic field",
      "classical main conjecture",
      "units modulo elliptic units coincides",
      "global units modulo elliptic units",
      "characteristic ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1125V"
    }
  }
}