{
  "id": "0911.4834",
  "version": "v2",
  "published": "2009-11-25T12:41:19.000Z",
  "updated": "2010-11-15T17:56:56.000Z",
  "title": "Torsors under tori and Néron models",
  "authors": [
    "Martin Bright"
  ],
  "comment": "10 pages",
  "journal": "Journal de Th\\'eorie des Nombres de Bordeaux 23 (2011), 309-321",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Let R be a Henselian discrete valuation ring with field of fractions K. If X is a smooth variety over K and G a torus over K, then we consider X-torsors under G. If XX/R is a model of X then, using a result of Brahm, we show that X-torsors under G extend to XX-torsors under a N\\'eron model of G if G is split by a tamely ramified extension of K. It follows that the evaluation map associated to such a torsor factors through reduction to the special fibre. In this way we can use the geometry of the special fibre to study the arithmetic of X.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-15T17:56:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G20",
      "14G05",
      "14F20",
      "11G25"
    ],
    "keywords": [
      "néron models",
      "special fibre",
      "evaluation map",
      "neron model",
      "henselian discrete valuation ring"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4834B"
    }
  }
}