{
  "id": "0705.3372",
  "version": "v2",
  "published": "2007-05-23T13:34:35.000Z",
  "updated": "2007-11-14T04:18:05.000Z",
  "title": "Rings of integers of type $K(π,1)$",
  "authors": [
    "Alexander Schmidt"
  ],
  "comment": "final version, to appear in documenta mathematica",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the Galois group $G_S(p)$ of the maximal $p$-extension unramified outside a finite $S$ of primes of a number field in the (tame) case, when no prime dividing $p$ is in $S$. We show that the cohomology of $G_S(p)$ is 'often' isomorphic to the etale cohomology of the scheme $\\Spec(\\O_k \\sm S)$, in particular, $G_S(p)$ is of cohomological dimension~2 then.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-14T04:18:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R34",
      "12G10"
    ],
    "keywords": [
      "galois group",
      "extension unramified outside",
      "number field",
      "etale cohomology",
      "isomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.3372S"
    }
  }
}