{
  "id": "1811.02250",
  "version": "v1",
  "published": "2018-11-06T09:32:33.000Z",
  "updated": "2018-11-06T09:32:33.000Z",
  "title": "Profinite groups with a cyclotomic $p$-orientation",
  "authors": [
    "Claudio Quadrelli",
    "Thomas Weigel"
  ],
  "comment": "34 pages",
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "Profinite groups with a cyclotomic $p$-orientation are introduced and studied. The special interest in this class of groups arises from the fact that any absolute Galois group $G_{K}$ of a field $K$ is indeed a profinite group with a cyclotomic $p$-orientation $\\theta_{K,p}\\colon G_{K}\\to\\mathbb{Z}_p^\\times$ which is even Bloch-Kato. The same is true for its maximal pro-$p$ quotient $G_{K}(p)$ provided the field $K$ contains a primitive $p^{th}$-root of unity. The class of cyclotomically $p$-oriented profinite groups (resp. pro-$p$ groups) which are Bloch-Kato is closed with respect to inverse limits, free product and certain fibre products. For profinite groups with a cyclotomic $p$-orientation the classical Artin-Schreier theorem holds. Moreover, Bloch-Kato pro-$p$ groups with a cyclotomic orientation satisfy a strong form of Tits' alternative, and the elementary type conjecture formulated by I. Efrat can be restated that the only finitely generated indecomposable torsion free Bloch-Kato pro-$p$ groups with a cyclotomic orientation should be Poincar\\'e duality pro-$p$ groups of dimension less or equal to $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-06T09:32:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "12G05"
    ],
    "keywords": [
      "profinite group",
      "elementary type conjecture",
      "absolute galois group",
      "generated indecomposable torsion free bloch-kato",
      "classical artin-schreier theorem holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}