{
  "id": "2007.02576",
  "version": "v1",
  "published": "2020-07-06T08:09:06.000Z",
  "updated": "2020-07-06T08:09:06.000Z",
  "title": "Hochschild homology and the derived de Rham complex revisited",
  "authors": [
    "Arpon Raksit"
  ],
  "comment": "69 pages",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We characterize two objects by universal property: the derived de Rham complex and Hochschild homology together with its Hochschild-Kostant-Rosenberg filtration. This involves endowing these objects with extra structure, built on notions of \"homotopy-coherent cochain complex\" and \"filtered circle action\" that we study here. We use these universal properties to give a conceptual proof of the statements relating Hochschild homology and the derived de Rham complex, in particular giving a new construction of the filtrations on cyclic, negative cyclic, and periodic cyclic homology that relate these invariants to derived de Rham cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-06T08:09:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rham complex",
      "universal property",
      "periodic cyclic homology",
      "homotopy-coherent cochain complex",
      "statements relating hochschild homology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 69,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}