{
  "id": "2209.00753",
  "version": "v1",
  "published": "2022-09-01T23:45:19.000Z",
  "updated": "2022-09-01T23:45:19.000Z",
  "title": "An estimate for F-jumping numbers via the roots of the Bernstein-Sato polynomial",
  "authors": [
    "Mircea Mustaţă"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AG",
    "math.AC"
  ],
  "abstract": "Given a smooth complex algebraic variety $X$ and a nonzero regular function $f$ on $X$, we give an effective estimate for the difference between the jumping numbers of $f$ and the $F$-jumping numbers of a reduction $f_p$ of $f$ to characteristic $p\\gg 0$, in terms of the roots of the Bernstein-Sato polynomial $b_f$ of $f$. As an application, we show that if $b_f$ has no roots of the form $-{\\rm lct}(f)-n$, with $n$ a positive integer, then the $F$-pure threshold of $f_p$ is equal to the log canonical threshold of $f$ for $p\\gg 0$ with $(p-1){\\rm lct}(f)\\in {\\mathbf Z}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-01T23:45:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A35",
      "14F18",
      "14F10"
    ],
    "keywords": [
      "bernstein-sato polynomial",
      "f-jumping numbers",
      "smooth complex algebraic variety",
      "nonzero regular function",
      "pure threshold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}