{
  "id": "1611.08139",
  "version": "v1",
  "published": "2016-11-24T11:14:04.000Z",
  "updated": "2016-11-24T11:14:04.000Z",
  "title": "Torsion pairs in silting theory",
  "authors": [
    "Lidia Angeleri Hügel",
    "Frederik Marks",
    "Jorge Vitória"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In the setting of compactly generated triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and only if the (co)silting object satisfies a purity assumption. Moreover, in the cosilting case the previous conditions are related to the coaisle of the t-structure being a definable subcategory. If we further assume our triangulated category to be algebraic, it follows that the heart of any nondegenerate compactly generated t-structure is a Grothendieck category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-24T11:14:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E15",
      "18E30",
      "18E40"
    ],
    "keywords": [
      "torsion pairs",
      "silting theory",
      "grothendieck category",
      "triangulated category",
      "nondegenerate compactly generated t-structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}