{
  "id": "1408.2678",
  "version": "v2",
  "published": "2014-08-12T09:44:12.000Z",
  "updated": "2014-12-28T07:53:54.000Z",
  "title": "Silting reduction and Calabi--Yau reduction of triangulated categories",
  "authors": [
    "Osamu Iyama",
    "Dong Yang"
  ],
  "comment": "47 pages. More results on t-structures added (in the new section 3) to further improve the proof of Theorem 5.9. Results in section 5 (section 4 in the preceding version) generalized from silting objects to silting subcategories",
  "categories": [
    "math.RT"
  ],
  "abstract": "It is shown that the silting reduction $\\ct/\\thick\\cp$ of a triangulated category $\\ct$ with respect to a presilting subcategory $\\cp$ can be realized as a certain subfactor category of $\\ct$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\\ct$ containing $\\cp$ and the set of (pre)silting subcategories of $\\ct/\\thick\\cp$. This is analogous to a result for Calabi--Yau reduction. This result is applied to show that Amiot--Guo--Keller's construction of $d$-Calabi--Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to Calabi--Yau reduction, and conversely, Calabi--Yau reduction lifts to silting reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-12T09:44:12.000Z",
      "abstract": "It is shown that the silting reduction $\\ct/\\thick\\cp$ of a triangulated category $\\ct$ with respect to a presilting subcategory $\\cp$ can be realised as a certain subfactor category of $\\ct$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\\ct$ containing $\\cp$ and the set of (pre)silting subcategories of $\\ct/\\thick\\cp$. This is analogous to a result for Calabi--Yau reduction. This result is applied to show that the Amiot--Guo--Keller construction of $d$-Calabi--Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to Calabi--Yau reduction, and conversely, Calabi--Yau reduction lifts to silting reduction.",
      "comment": "40 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-28T07:53:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "18E30",
      "16G99",
      "13F60"
    ],
    "keywords": [
      "silting reduction",
      "triangulated category",
      "calabi-yau reduction lifts",
      "subcategory",
      "silting subcategories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2678I"
    }
  }
}