{
  "id": "2001.08923",
  "version": "v1",
  "published": "2020-01-24T09:24:18.000Z",
  "updated": "2020-01-24T09:24:18.000Z",
  "title": "On accumulation points of $F$-pure thresholds on regular local rings",
  "authors": [
    "Kenta Sato"
  ],
  "comment": "18pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Blickle, Musta\\c{t}\\u{a} and Smith proposed two conjectures on the limits of $F$-pure thresholds. One conjecture asks whether or not the limit of a sequence of $F$-pure thresholds of principal ideals on regular local rings of fixed dimension can be written as an $F$-pure thresholds in lower dimension. Another conjecture predicts that any $F$-pure threshold of a formal power series can be written as the $F$-pure threshold of a polynomial. In this paper, we prove that the first conjecture has a counterexample but a weaker statement still holds. We also give a partial affirmative answer to the second conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-24T09:24:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A35",
      "14B05",
      "13B25"
    ],
    "keywords": [
      "pure threshold",
      "regular local rings",
      "accumulation points",
      "formal power series",
      "first conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}