{
  "id": "1210.1522",
  "version": "v4",
  "published": "2012-10-04T17:21:45.000Z",
  "updated": "2016-06-28T12:29:09.000Z",
  "title": "Models of torsors over curves",
  "authors": [
    "Marco Antei"
  ],
  "comment": "This paper has been withdrawn: it contained a mistake. It has been corrected and the results can now be found in \"Models of torsors and the fundamental group scheme\" (by M. Antei and M. Emsalem)",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let $R$ be a complete discrete valuation ring with fraction field $K$ and with algebraically closed residue field. Let $X$ be a faithfully flat $R$-scheme of finite type of relative dimension 1 and $G$ be any affine $K$-group scheme of finite type. We prove that every $G$-torsor $Y$ over the generic fibre $X_{\\eta}$ of $X$ can be extended to a torsor over ${X'}$ under the action of an affine and flat $K$-group scheme of finite type $G'$ where $X'$ is obtained by $X$ after a finite number of N\\'eron blowing ups. Moreover if $G$ is finite and \\'etale (resp. admits a finite and flat model) we find $X'$ such that $G'$ is finite and \\'etale (resp. finite and flat) after, if necessary, extending scalars. We provide examples explaining the new techniques.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-07T17:16:35.000Z",
      "comment": "21 pages, contains corrections",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2016-06-28T12:29:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L30",
      "14L15",
      "11G99"
    ],
    "keywords": [
      "finite type",
      "group scheme",
      "complete discrete valuation ring",
      "algebraically closed residue field",
      "fraction field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.1522A"
    }
  }
}