{
  "id": "0905.1364",
  "version": "v6",
  "published": "2009-05-09T02:21:24.000Z",
  "updated": "2011-01-27T15:54:04.000Z",
  "title": "Quotients of absolute Galois groups which determine the entire Galois cohomology",
  "authors": [
    "Sunil K. Chebolu",
    "Ido Efrat",
    "Ján Mináč"
  ],
  "comment": "16 pages, Final version, To appear in Mathematische Annalen",
  "categories": [
    "math.GR",
    "math.AT",
    "math.NT"
  ],
  "abstract": "For prime power $q=p^d$ and a field $F$ containing a root of unity of order $q$ we show that the Galois cohomology ring $H^*(G_F,\\dbZ/q)$ is determined by a quotient $G_F^{[3]}$ of the absolute Galois group $G_F$ related to its descending $q$-central sequence. Conversely, we show that $G_F^{[3]}$ is determined by the lower cohomology of $G_F$. This is used to give new examples of pro-$p$ groups which do not occur as absolute Galois groups of fields.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-01-27T15:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "12F10",
      "12E30"
    ],
    "keywords": [
      "absolute galois group",
      "entire galois cohomology",
      "lower cohomology",
      "central sequence",
      "prime power"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1364C"
    }
  }
}