{
  "id": "1608.03112",
  "version": "v1",
  "published": "2016-08-10T10:07:48.000Z",
  "updated": "2016-08-10T10:07:48.000Z",
  "title": "Iwasawa theory of Rubin-Stark units and class group",
  "authors": [
    "Youness Mazigh"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be a totally real number field of degree $r=[K:\\mathbb{Q}]$ and let $p$ be an odd rational prime. Let $K_{\\infty}$ denote the cyclotomic $\\mathbb{Z}_{p}$-extension of $K$ and let $L_{\\infty}$ be a finite extension of $K_{\\infty}$, abelian over $K$. In this article, we extend results of \\cite{Kazim109} relating characteristic ideal of the $\\chi$-quotient of the projective limit of the ideal class groups to the $\\chi$-quotient of the projective limit of the $r$-th exterior power of units modulo Rubin-Stark units, in the non semi-simple case, for some $\\overline{\\mathbb{Q}_{p}}$-irreductible characters $\\chi$ of $\\mathrm{Gal}(L_{\\infty}/K_{\\infty})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T10:07:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R27",
      "11R29",
      "11R42"
    ],
    "keywords": [
      "iwasawa theory",
      "units modulo rubin-stark units",
      "totally real number field",
      "projective limit",
      "ideal class groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}