{
  "id": "0801.2103",
  "version": "v1",
  "published": "2008-01-14T16:00:54.000Z",
  "updated": "2008-01-14T16:00:54.000Z",
  "title": "On the K(π,1)-property for rings of integers in the mixed case",
  "authors": [
    "Alexander Schmidt"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the Galois group G_S(p) of the maximal p-extension unramified outside a finite set S of primes of a number field in the (mixed) case, when there are primes dividing p inside and outside S. We show that the cohomology of G_S(p) is \"often\" isomorphic to the etale cohomology of the scheme Spec(O_k S), in particular, G_S(p) is of cohomological dimension 2 then. We deduce this from the results in our previous paper \"Rings of integers of type K(\\pi,1)\" (arXiv:0705.3372), which mainly dealt with the tame case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-14T16:00:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R34",
      "12G10"
    ],
    "keywords": [
      "mixed case",
      "maximal p-extension unramified outside",
      "galois group",
      "number field",
      "tame case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.2103S"
    }
  }
}