{
  "id": "1903.08007",
  "version": "v1",
  "published": "2019-03-19T14:09:42.000Z",
  "updated": "2019-03-19T14:09:42.000Z",
  "title": "A comparison between obstructions to local-global principles over semiglobal fields",
  "authors": [
    "David Harbater",
    "Julia Hartmann",
    "Valentijn Karemaker",
    "Florian Pop"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the valuation theory of the function field, or from the geometry of a regular model of the function field. Our results compare the corresponding obstructions, proving in particular that a local-global principle with respect to valuations implies a local-global principle with respect to a sufficiently fine regular model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-19T14:09:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F30",
      "14G05",
      "14H25",
      "14G27",
      "11E72"
    ],
    "keywords": [
      "local-global principle",
      "semiglobal fields",
      "obstructions",
      "comparison",
      "sufficiently fine regular model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}