{
  "id": "0802.2272",
  "version": "v2",
  "published": "2008-02-15T19:40:37.000Z",
  "updated": "2008-02-18T09:13:06.000Z",
  "title": "Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases",
  "authors": [
    "Mahesh Kakde"
  ],
  "comment": "49 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\\mathbbZ_p$ . First we assume that $H$ is finite and compute the Whitehead group of the Iwasawa algebra, $\\Lambda(G)$, of $G$. We also prove some results about certain localisation of $\\Lambda(G)$ needed in Iwasawa theory. Let $F$ be a totally real number field and let $F_{\\infty}$ be an admissible $p$-adic Lie extension of $F$ with Galois group $G$. The computation of the Whitehead groups are used to show that the Main Conjecture for the extension $F_{\\infty}/F$ can be deduced from certain congruences between abelian $p$-adic zeta functions of Delige and Ribet. We prove these congruences with certain assumptions on $G$. This gives a proof of the Main Conjecture in many interesting cases such as $\\mathbb{Z}_p\\rtimes",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-18T09:13:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R23",
      "11R80"
    ],
    "keywords": [
      "totally real number field",
      "main conjecture",
      "noncommutative iwasawa theory",
      "whitehead group",
      "adic lie group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.2272K"
    }
  }
}