{
  "id": "1808.01705",
  "version": "v1",
  "published": "2018-08-06T01:17:31.000Z",
  "updated": "2018-08-06T01:17:31.000Z",
  "title": "Relations in the maximal pro-$p$ quotients of absolute Galois groups",
  "authors": [
    "Jan Minac",
    "Michael Rogelstad",
    "Nguyen Duy Tan"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We observe that some basic but fundamental constructions in Galois theory can be used to obtain some interesting restrictions on the structure of Galois groups of maximal $p$-extensions of fields containing a primitive $p$th root of unity. This is an extension of some significant ideas of Demushkin, Labute and Serre from local fields to all fields containing a primitive $p$th root of unity. Our techniques use certain natural simple Galois extensions together with some considerations in Galois cohomology and Massey products.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-06T01:17:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absolute galois groups",
      "natural simple galois extensions",
      "th root",
      "local fields",
      "massey products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}