{
  "id": "2012.08500",
  "version": "v2",
  "published": "2020-12-15T18:51:05.000Z",
  "updated": "2022-04-27T06:26:31.000Z",
  "title": "Arithmetic Orr invariants of absolute Galois groups",
  "authors": [
    "Hisatoshi Kodani",
    "Yuji Terashima"
  ],
  "comment": "65 pages; table of contents is inserted; several minor errors are corrected; minor modifications in p.26, p.29, p.56; to appear in Int. Math. Res. Not. IMRN",
  "categories": [
    "math.NT"
  ],
  "abstract": "Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-$\\ell$ analogue of Orr invariants for a Galois element associated with Galois action on \\'etale fundamental groups of punctured projective lines. At the same time, we also introduce pro-$\\ell$ Orr space as an arithmetic analogue of Orr space whose third homotopy group is a target group of Orr invariant. We then determine its rank as $\\mathbb{Z}_{\\ell}$-module following Igusa-Orr's computation. Moreover, we investigate its relation with Ellenberg's obstruction to $\\pi_1$-sections associated with lower central series filtration in the context of Grothendieck's section conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-04-27T06:26:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "14F35",
      "20E18",
      "20F34",
      "20F36",
      "55S30",
      "57K10"
    ],
    "keywords": [
      "absolute galois groups",
      "arithmetic orr invariants",
      "orr space",
      "lower central series filtration",
      "third homotopy group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}