{
  "id": "1502.02349",
  "version": "v1",
  "published": "2015-02-09T04:17:42.000Z",
  "updated": "2015-02-09T04:17:42.000Z",
  "title": "Relative Singularity Categories",
  "authors": [
    "Huanhuan Li",
    "Zhaoyong Huang"
  ],
  "comment": "17 pages, to appear in Journal of Pure and Applied Algebra",
  "doi": "10.1016/j.jpaa.2015.02.009",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We study the properties of the relative derived category $D_{\\mathscr{C}}^{b}$($\\mathscr{A}$) of an abelian category $\\mathscr{A}$ relative to a full and additive subcategory $\\mathscr{C}$. In particular, when $\\mathscr{A}=A{\\text -}\\mod$ for a finite-dimensional algebra $A$ over a field and $\\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\\mod$ which is admissible and closed under direct summands, the $\\mathscr{C}$-singularity category $D_{\\mathscr{C}{\\text sg}}$($\\mathscr{A}$)=$D_{\\mathscr{C}}^{b}$($\\mathscr{A}$)/$K^{b}(\\mathscr{C})$ is studied. We give a sufficient condition when this category is triangulated equivalent to the stable category of the Gorenstein category $\\mathscr{G}(\\mathscr{C})$ of $\\mathscr{C}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-09T04:17:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singularity category",
      "relative singularity categories",
      "direct summands",
      "sufficient condition",
      "contravariantly finite subcategory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}