{
  "id": "2301.03112",
  "version": "v1",
  "published": "2023-01-08T21:26:00.000Z",
  "updated": "2023-01-08T21:26:00.000Z",
  "title": "Periodic Cyclic Homology over Q",
  "authors": [
    "Konrad Bals"
  ],
  "comment": "17 pages. Comments welcome!",
  "categories": [
    "math.AT",
    "math.AG"
  ],
  "abstract": "Let $X$ be a derived scheme over an animated commutative ring of characteristic 0. We give a complete description of the periodic cyclic homology of $X$ in terms of the Hodge completed derived de Rham complex of $X$. In particular this extends earlier computations of Loday-Quillen to non-smooth algebras. Moreover, we get an explicit condition on the Hodge completed derived de Rham complex, that makes the HKR-filtration on periodic cyclic homology constructed by Antieau and Bhatt-Lurie exhaustive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-08T21:26:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic cyclic homology",
      "rham complex",
      "extends earlier computations",
      "complete description",
      "explicit condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}