{
  "id": "2303.04120",
  "version": "v3",
  "published": "2023-03-07T18:30:59.000Z",
  "updated": "2023-06-12T10:26:52.000Z",
  "title": "Galois cohomology of reductive groups over global fields",
  "authors": [
    "Mikhail Borovoi",
    "Tasho Kaletha"
  ],
  "comment": "V1,2: 43 pages. V3: 58 pages, a new section added",
  "categories": [
    "math.NT",
    "math.AG",
    "math.GR",
    "math.RT"
  ],
  "abstract": "Generalizing Tate's results for tori, we give closed formulas for the abelian Galois cohomology groups H^1_{ab}(F,G) and H^2_{ab}(F,G) of a connected reductive group G over a global field F, and obtain formulas, suitable for computer calculatios, for the first nonabelian Galois cohomology set H^1(F,G) of G and for the second Galois cohomology group H^2(F,T) of an F-torus T.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2023-06-12T10:26:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E72",
      "20G10",
      "20G25",
      "20G30"
    ],
    "keywords": [
      "global field",
      "reductive group",
      "first nonabelian galois cohomology set",
      "abelian galois cohomology groups",
      "second galois cohomology group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}