{
  "id": "1203.5657",
  "version": "v4",
  "published": "2012-03-26T13:22:16.000Z",
  "updated": "2013-09-07T07:29:42.000Z",
  "title": "Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras",
  "authors": [
    "Steffen Koenig",
    "Dong Yang"
  ],
  "comment": "32 pages. Some sections are removed",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations. The results are valid for finite-dimensional algebras. A concrete example is given to illustrate how these correspondences help to compute the space of Bridgeland's stability conditions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-09-07T07:29:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "structures",
      "finite-dimensional algebras",
      "simple-minded collections",
      "silting objects",
      "bridgelands stability conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5657K"
    }
  }
}