{
  "id": "1702.04550",
  "version": "v1",
  "published": "2017-02-15T11:18:23.000Z",
  "updated": "2017-02-15T11:18:23.000Z",
  "title": "Singularity categories of derived categories of hereditary algebras are derived categories",
  "authors": [
    "Yuta Kimura"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that for the path algebra $A$ of an acyclic quiver, the singularity category of the derived category $\\mathsf{D}^{\\rm b}(\\mathsf{mod}\\,A)$ is triangle equivalent to the derived category of the functor category of $\\underline{\\mathsf{mod}}\\,A$, that is, $\\mathsf{D}_{\\rm sg}(\\mathsf{D}^{\\rm b}(\\mathsf{mod}\\,A))\\simeq \\mathsf{D}^{\\rm b}(\\mathsf{mod}(\\underline{\\mathsf{mod}}\\,A))$. This extends a result of Iyama-Oppermann for the path algebra $A$ of a Dynkin quiver. An important step is to establish a functor category analog of Happel's triangle equivalence for repetitive algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-15T11:18:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derived category",
      "singularity category",
      "hereditary algebras",
      "path algebra",
      "functor category analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}