{
  "id": "1102.3031",
  "version": "v1",
  "published": "2011-02-15T10:37:58.000Z",
  "updated": "2011-02-15T10:37:58.000Z",
  "title": "Global Units Modulo Elliptic Units and 2-Ideal Class Groups",
  "authors": [
    "Stéphane Viguié"
  ],
  "comment": "16 pages",
  "journal": "International Journal of Number Theory, volume 8 no.3, pp. 569-588 (2012)",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let p\\in\\{2,3\\}, and let k be an imaginary quadratic field in which p decomposes into two distinct primes \\mathfrak{p} and \\bar{\\mathfrak{p}}. Let k_\\infty be the unique Z_p-extension of k which is unramified outside of \\mathfrak{p}, and let K_\\infty be a finite extension of k_\\infty, abelian over k. We prove that in K_\\infty, the projective limit of the p-class group and the projective limit of units modulo elliptic units share the same \\mu-invariant and the same \\lambda-invariant. Then we prove that up to a constant, the characteristic ideal of the projective limit of the p-class group coincides with the characteristic ideal of the projective limit of units modulo elliptic units.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-15T10:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G16",
      "11R23",
      "11R65"
    ],
    "keywords": [
      "global units modulo elliptic units",
      "class groups",
      "projective limit",
      "units modulo elliptic units share",
      "p-class group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.3031V"
    }
  }
}