{
  "id": "2406.17355",
  "version": "v1",
  "published": "2024-06-25T08:14:18.000Z",
  "updated": "2024-06-25T08:14:18.000Z",
  "title": "Local-global principle for over semiglobal fields",
  "authors": [
    "Philippe Gille",
    "Raman Parimala"
  ],
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We compare different local-global principles for torsors under a reductive group G defined over a semiglobal field F. In particular if the F-group G s a retract rational F-variety, we prove that the local global principle holds for the completions with respect to divisorial valuations of F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-25T08:14:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local-global principle",
      "semiglobal field",
      "local global principle holds",
      "retract rational f-variety",
      "divisorial valuations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}