{
  "id": "1412.7685",
  "version": "v1",
  "published": "2014-12-24T15:21:54.000Z",
  "updated": "2014-12-24T15:21:54.000Z",
  "title": "Cohomology of absolute Galois groups",
  "authors": [
    "Claudio Quadrelli"
  ],
  "comment": "Ph.D. thesis at Western University (Canada) and Universit\\`a di Milano-Bicocca (Italy), 103 pages, 1 figure",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "The main problem this thesis deals with is the characterization of profinite groups which are realizable as absolute Galois groups of fields: this is currently one of the major problems in Galois theory. Usually one reduces the problem to the pro-$p$ case, i.e., one would like to know which pro-$p$ groups occur as maximal pro-$p$ Galois groups, i.e., maximal pro-$p$ quotients of absolute Galois groups. Indeed, pro-$p$ groups are easier to deal with than general profinite groups, yet they carry a lot of information on the whole absolute Galois group. We define a new class of pro-$p$ groups, called Bloch-Kato pro-$p$ group, whose Galois cohomology satisfies the consequences of the Bloch-Kato conjecture. Also we introduce the notion of cyclotomic orientation for a pro-$p$ group. With this approach, we are able to recover new substantial information about the structure of maximal pro-$p$ Galois groups, and in particular on $\\theta$-abelian pro-$p$ groups, which represent the \"upper bound\" of such groups. Also, we study the restricted Lie algebra and the universal envelope induced by the Zassenhaus filtration of a maximal pro-$p$ Galois group, and their relations with Galois cohomology via Koszul duality. Altogether, this thesis provides a rather new approach to maximal pro-$p$ Galois groups, besides new substantial results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-24T15:21:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "20J06",
      "20E18",
      "12F10"
    ],
    "keywords": [
      "absolute galois group",
      "general profinite groups",
      "galois cohomology satisfies",
      "bloch-kato conjecture",
      "substantial results"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 103,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.7685Q"
    }
  }
}