{
  "id": "1007.3428",
  "version": "v1",
  "published": "2010-07-20T14:06:16.000Z",
  "updated": "2010-07-20T14:06:16.000Z",
  "title": "Filtrations in abelian categories with a tilting object of homological dimension two",
  "authors": [
    "Bernt Tore Jensen",
    "Dag Madsen",
    "Xiuping Su"
  ],
  "categories": [
    "math.RT",
    "math.KT"
  ],
  "abstract": "We consider filtrations of objects in an abelian category $\\catA$ induced by a tilting object $T$ of homological dimension at most two. We define three disjoint subcategories with no maps between them in one direction, such that each object has a unique filtation with factors in these categories. This filtration coincides with the the classical two-step filtration induced by torsion pairs in dimension one. We also give a refined filtration, using the derived equivalence between the derived categories of $\\catA$ and the module category of $End_\\catA (T)^{op}$. The factors of this filtration consist of kernel and cokernels of maps between objects which are quasi-isomorphic to shifts of $End_\\catA (T)^{op}$-modules via the derived equivalence $\\mathbb{R}Hom_\\catA(T,-)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-20T14:06:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G20"
    ],
    "keywords": [
      "abelian category",
      "homological dimension",
      "tilting object",
      "derived equivalence",
      "filtration consist"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.3428T"
    }
  }
}