{
  "id": "0804.2828",
  "version": "v2",
  "published": "2008-04-17T14:34:27.000Z",
  "updated": "2009-08-12T10:54:03.000Z",
  "title": "On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields",
  "authors": [
    "Jennifer Johnson-Leung",
    "Guido Kings"
  ],
  "comment": "38 pages, completely revised version, inaccuracies and typos fixed",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The Iwasawa main conjecture fields has been an important tool to study the arithmetic of special values of $L$-functions of Hecke characters of imaginary quadratic fields. To obtain the finest possible invariants it is important to know the main conjecture for all prime numbers $p$ and also to have an equivariant version at disposal. In this paper we first prove the main conjecture for imaginary quadratic fields for all prime numbers $p$, improving earlier results by Rubin. From this we deduce the equivariant main conjecture in the case that a certain $\\mu$-invariant vanishes. For prime numbers $p\\nmid 6$ which split in $K$, this is a theorem by a result of Gillard.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-12T10:54:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "non-equivariant main conjecture",
      "prime numbers",
      "iwasawa main conjecture fields",
      "hecke characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.2828J"
    }
  }
}