{
  "id": "2108.12349",
  "version": "v1",
  "published": "2021-08-27T15:24:47.000Z",
  "updated": "2021-08-27T15:24:47.000Z",
  "title": "Local-global principles for constant reductive groups over semi-global fields",
  "authors": [
    "Jean-Louis Colliot-Thélène",
    "David Harbater",
    "Julia Hartmann",
    "Daniel Krashen",
    "R. Parimala",
    "V. Suresh"
  ],
  "comment": "58 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the semiglobal field under which the local-global principle holds, and we compute the obstruction to the local-global principle in certain classes of examples. Using our description of the obstruction, we give the first example of a semisimple simply connected group over a semi-global field where the local-global principle fails. Our methods include patching and R-equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-27T15:24:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E72",
      "12G05",
      "14G05",
      "14H25",
      "20G15",
      "14G27"
    ],
    "keywords": [
      "semi-global field",
      "constant reductive groups",
      "reductive linear algebraic groups",
      "local-global principle holds",
      "study local-global principles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}