{
  "id": "1106.0207",
  "version": "v1",
  "published": "2011-06-01T15:30:29.000Z",
  "updated": "2011-06-01T15:30:29.000Z",
  "title": "Log canonical thresholds, F-pure thresholds, and non-standard extensions",
  "authors": [
    "Bhargav Bhatt",
    "Daniel J. Hernandez",
    "Lance E. Miller",
    "Mircea Mustata"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "We present a new relation between an invariant of singularities in characteristic zero (the log canonical threshold) and an invariant of singularities defined via the Frobenius morphism in positive characteristic (the F-pure threshold). We show that the set of limit points of sequences of the form (c_p), where c_p is the F-pure threshold of an ideal on an n-dimensional smooth variety in characteristic p, coincides with the set of log canonical thresholds of ideals on n-dimensional smooth varieties in characteristic zero. We prove this by combining results of Hara and Yoshida with non-standard constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-01T15:30:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A35",
      "13L05",
      "14B05",
      "14F18"
    ],
    "keywords": [
      "log canonical threshold",
      "f-pure threshold",
      "non-standard extensions",
      "n-dimensional smooth variety",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0207B"
    }
  }
}