{
  "id": "1704.06484",
  "version": "v1",
  "published": "2017-04-21T11:19:41.000Z",
  "updated": "2017-04-21T11:19:41.000Z",
  "title": "Silting and cosilting classes in derived categories",
  "authors": [
    "Frederik Marks",
    "Jorge Vitória"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are precisely the resolving and definable subcategories of the module category whose Ext-orthogonal class has bounded injective dimension. In this article, we prove a derived counterpart of the statements above in the context of silting theory. Silting and cosilting complexes in the derived category of a ring generalise tilting and cotilting modules. They give rise to subcategories of the derived category, called silting and cosilting classes, which are part of both a t-structure and a co-t-structure. We characterise these subcategories: silting classes are precisely those which are intermediate and Ext-orthogonal classes to a set of compact objects, and cosilting classes are precisely the cosuspended, definable and co-intermediate subcategories of the derived category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-21T11:19:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "18E30",
      "18E40"
    ],
    "keywords": [
      "derived category",
      "cosilting classes",
      "ext-orthogonal class",
      "co-intermediate subcategories",
      "compact objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}