{
  "id": "2207.13967",
  "version": "v1",
  "published": "2022-07-28T09:13:35.000Z",
  "updated": "2022-07-28T09:13:35.000Z",
  "title": "Extendability of differential forms via Cartier operators",
  "authors": [
    "Tatsuro Kawakami"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $(X, B)$ be a pair of a normal variety over a perfect field of positive characteristic and a reduced divisor. We prove that if the Cartier isomorphism on the log smooth locus of $(X,B)$ extends to the whole $X$, then $(X,B)$ satisfies the logarithmic extension theorem. As applications, we show that the logarithmic (resp.~regular) extension theorem holds for a quotient singularity by a linearly reductive group scheme (resp.~a finite group scheme order prime to the characteristic). We also prove that the logarithmic extension theorem for one-forms for singularities of higher codimension holds under assumptions about Serre's condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-28T09:13:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A35",
      "14F10",
      "14B05"
    ],
    "keywords": [
      "differential forms",
      "cartier operators",
      "logarithmic extension theorem",
      "finite group scheme order prime",
      "extendability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}