{
  "id": "2203.16232",
  "version": "v1",
  "published": "2022-03-30T12:08:53.000Z",
  "updated": "2022-03-30T12:08:53.000Z",
  "title": "Massey products in Galois cohomology and the Elementary Type Conjecture",
  "authors": [
    "Claudio Quadrelli"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime. We prove that a positive solution to Efrat's Elementary Type Conjecture implies a positive solution to a strengthened version of Minac-T\\^an's Massey Vanishing Conjecture. Consequently, the maximal pro-$p$ Galois group of a field $K$ containing a root of 1 of order $p$ satisfies the strong $n$-Massey vanishing property in several relevant cases, e.g.: $K$ is a local field; $K$ is a PAC field; $K$ is a $p$-rigid field; $K$ is algebraic extension of a global field with finitely generated maximal pro-$p$ Galois group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-30T12:08:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "20E18",
      "20J06",
      "12F10"
    ],
    "keywords": [
      "galois cohomology",
      "massey products",
      "efrats elementary type conjecture implies",
      "galois group",
      "positive solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}