{
  "id": "2106.03675",
  "version": "v1",
  "published": "2021-06-07T14:56:55.000Z",
  "updated": "2021-06-07T14:56:55.000Z",
  "title": "Mild pro-p groups and the Koszulity conjectures",
  "authors": [
    "Jan Minac",
    "Federico Pasini",
    "Claudio Quadrelli",
    "Nguyen Duy Tân"
  ],
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "Let $p$ be a prime, and $\\mathbb{F}_p$ the field with $p$ elements. We prove that if $G$ is a mild pro-$p$ group with quadratic $\\mathbb{F}_p$-cohomology algebra $H^\\bullet(G,\\mathbb{F}_p)$, then the algebras $H^\\bullet(G,\\mathbb{F}_p)$ and $\\mathrm{gr}\\mathbb{F}_p[\\![G]\\!]$ - the latter being induced by the quotients of consecutive terms of the $p$-Zassenhaus filtration of $G$ - are both Koszul, and they are quadratically dual to each other. Consequently, if the maximal pro-$p$ Galois group of a field is mild, then Positselski's and Weigel's Koszulity conjectures hold true for such a field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-07T14:56:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12G05",
      "16S37",
      "20E18",
      "12F10",
      "20J06"
    ],
    "keywords": [
      "mild pro-p groups",
      "weigels koszulity conjectures hold true",
      "cohomology algebra",
      "galois group",
      "zassenhaus filtration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}