{
  "id": "2307.11746",
  "version": "v1",
  "published": "2023-07-21T17:56:07.000Z",
  "updated": "2023-07-21T17:56:07.000Z",
  "title": "Foliations and Galois Theory in Positive Characteristic",
  "authors": [
    "Przemyslaw Grabowski"
  ],
  "comment": "29 pages. Comments welcome!",
  "categories": [
    "math.AG",
    "math.AC",
    "math.RA"
  ],
  "abstract": "We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between separable field extensions and purely inseparable field extensions. Specifically, it serves as a progression towards gaining a deeper comprehension of a foliation theory on varieties in positive characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-21T17:56:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F15",
      "12F20",
      "13B05",
      "13N10",
      "13N15",
      "16S32"
    ],
    "keywords": [
      "positive characteristic",
      "galois theory",
      "purely inseparable field extensions",
      "galois-type correspondence",
      "differential operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}