{
  "id": "1904.03156",
  "version": "v1",
  "published": "2019-04-05T16:51:40.000Z",
  "updated": "2019-04-05T16:51:40.000Z",
  "title": "On the decomposition of the De Rham complex on formal schemes",
  "authors": [
    "Leovigildo Alonso",
    "Ana Jeremias",
    "Marta Perez"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that, for a pseudo-proper smooth noetherian formal scheme $\\mathfrak{X}$ over a positive characteristic field, its truncated De Rham complex up to the characteristic $p$ is decomposable. Moreover, if the dimension of $\\mathfrak{X}$ is exactly $p$, then the full De Rham complex is decomposable. Along the way we establish the Cartier isomorphism associated to a smooth morphism of positive characteristic noetherian formal schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-05T16:51:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F40",
      "14F05",
      "14B20"
    ],
    "keywords": [
      "rham complex",
      "pseudo-proper smooth noetherian formal scheme",
      "positive characteristic noetherian formal schemes",
      "decomposition",
      "positive characteristic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}