{
  "id": "0803.4147",
  "version": "v2",
  "published": "2008-03-28T15:25:37.000Z",
  "updated": "2009-03-01T19:57:51.000Z",
  "title": "Principalization of ideals in abelian extensions of number fields",
  "authors": [
    "Sebastien Bosca",
    "Georges Gras",
    "Jean-François Jaulent"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We give the complete proof of a conjecture of Georges Gras which claims that, for any extension $K/k$ of number fields in which at least one infinite place is totally split, every ideal $I$ of $K$ principalizes in the compositum $Kk^{ab}$ of $K$ with the maximal abelian extension $k^{ab}$ of $k$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-03-01T19:57:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R27",
      "11R37"
    ],
    "keywords": [
      "number fields",
      "principalization",
      "maximal abelian extension",
      "infinite place",
      "georges gras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.4147B"
    }
  }
}