{
  "id": "2006.01677",
  "version": "v1",
  "published": "2020-06-02T14:50:22.000Z",
  "updated": "2020-06-02T14:50:22.000Z",
  "title": "Tilting theory of noetherian algebras",
  "authors": [
    "Yuta Kimura"
  ],
  "comment": "26 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "For a ring $\\Lambda$ with a Krull-Schmidt homotopy category, we study mutation theory on $2$-term silting complexes. As a consequence, mutation works when $\\Lambda$ is a complete noetherian algebra, that is, a module-finite algebra over a commutative complete local noetherian ring $R$. By using results on $2$-term silting complexes of such noetherian algebras and $\\tau$-tilting theory of Artin algebras, we study torsion classes of the module category of a noetherian algebra. When $R$ has Krull dimension one, the set of torsion classes of $\\Lambda$ is decomposed into subsets so that each subset bijectively corresponds to a certain subset of the set of torsion classes of Artin algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-02T14:50:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tilting theory",
      "complete local noetherian ring",
      "term silting complexes",
      "artin algebras",
      "commutative complete local noetherian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}