{
  "id": "2401.02057",
  "version": "v1",
  "published": "2024-01-04T04:42:29.000Z",
  "updated": "2024-01-04T04:42:29.000Z",
  "title": "$q$-de Rham complexes of higher level",
  "authors": [
    "Kimihiko Li"
  ],
  "comment": "64 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on higher-level $q$-crystalline site, which was introduced in the previous article of the author. One complex is the $q$-analog of the higher de Rham complex constructed by Miyatani, and another complex is the $q$-analog of the jet complex constructed by Le Stum-Quir\\'os. The complexes we constructed can also be regarded as the higher-level analogs of the $q$-de Rham complex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-04T04:42:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F30",
      "14F20"
    ],
    "keywords": [
      "rham complex",
      "higher level",
      "jet complex",
      "crystalline site",
      "complete crystals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}