{
  "id": "2011.03233",
  "version": "v1",
  "published": "2020-11-06T08:40:07.000Z",
  "updated": "2020-11-06T08:40:07.000Z",
  "title": "Two families of pro-p groups that are not absolute Galois groups",
  "authors": [
    "Claudio Quadrelli"
  ],
  "categories": [
    "math.NT",
    "math.GR"
  ],
  "abstract": "Let $p$ be a prime. We produce two new families of pro-$p$ groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-$p$ groups. Moreover, we show in these families one has one-relator pro-$p$ groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-06T08:40:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "20E18",
      "20J06",
      "12F10"
    ],
    "keywords": [
      "pro-p groups",
      "galois cohomology",
      "absolute galois groups employing",
      "rost-voevodsky theorem",
      "massey products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}