{
  "id": "1204.6421",
  "version": "v2",
  "published": "2012-04-28T16:56:37.000Z",
  "updated": "2013-09-30T09:05:49.000Z",
  "title": "Dimensions of triangulated categories with respect to subcategories",
  "authors": [
    "Takuma Aihara",
    "Tokuji Araya",
    "Osamu Iyama",
    "Ryo Takahashi",
    "Michio Yoshiwaki"
  ],
  "comment": "16 pages, to appear in J. Algebra",
  "categories": [
    "math.RT",
    "math.AC",
    "math.RA"
  ],
  "abstract": "This paper introduces the concept of the dimension of a triangulated category with respect to a fixed full subcategory. For the bounded derived category of an abelian category, upper bounds of the dimension with respect to a contravariantly finite subcategory and a resolving subcategory are given. Our methods not only recover some known results on the dimensions of derived categories in the sense of Rouquier, but also apply to various commutative and non-commutative noetherian rings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-30T09:05:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangulated category",
      "abelian category",
      "fixed full subcategory",
      "upper bounds",
      "contravariantly finite subcategory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.6421A"
    }
  }
}