{
  "id": "0805.3753",
  "version": "v2",
  "published": "2008-05-24T09:45:14.000Z",
  "updated": "2014-09-25T17:05:14.000Z",
  "title": "Birational geometry and localisation of categories",
  "authors": [
    "Bruno Kahn",
    "R. Sujatha"
  ],
  "comment": "65 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "This version contains substantial improvements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-24T09:45:14.000Z",
      "abstract": "We explore the relationships between the notions of places and rational maps in birational geometry. In particular, over a field F of characteristic 0, we show that in the category of smooth varieties localised with respect to birational morphisms, the set of morphisms from a variety X to a proper variety Y is the set of R-equivalence classes Y(F(X))/R.",
      "comment": "69 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-25T17:05:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "18F99"
    ],
    "keywords": [
      "birational geometry",
      "localisation",
      "r-equivalence classes",
      "birational morphisms",
      "rational maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 65,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.3753K"
    }
  }
}