{
  "id": "2406.08017",
  "version": "v1",
  "published": "2024-06-12T09:17:59.000Z",
  "updated": "2024-06-12T09:17:59.000Z",
  "title": "The defect of weak approximation for a reductive group over a global field",
  "authors": [
    "Mikhail Borovoi"
  ],
  "comment": "12 pages; comments are welcome!",
  "categories": [
    "math.RT",
    "math.AG",
    "math.GR",
    "math.NT"
  ],
  "abstract": "Using ideas of Sansuc and of Colliot-Th\\'el\\`ene and a result of Tate, we compute the defect of weak approximation for a reductive group G over a global field K in terms of the algebraic fundamental group of G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-12T09:17:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E72",
      "20G10",
      "20G20",
      "20G25",
      "20G30"
    ],
    "keywords": [
      "weak approximation",
      "global field",
      "reductive group",
      "algebraic fundamental group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}