{
  "id": "1603.02858",
  "version": "v1",
  "published": "2016-03-09T11:53:51.000Z",
  "updated": "2016-03-09T11:53:51.000Z",
  "title": "Semi-orthogonal decomposition of GIT quotient stacks",
  "authors": [
    "Špela Špenko",
    "Michel Van den Bergh"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "If G is a reductive group which acts on a linearized smooth scheme $X$ then we show that under suitable standard conditions the derived category of coherent sheaves of the corresponding GIT quotient stack $X^{ss}/G$ has a semi-orthogonal decomposition consisting of derived categories of coherent sheaves of rings on the categorical quotient $X^{ss}/\\!/G$ which are locally of finite global dimension. One of the components of the decomposition is a certain non-commutative resolution of $X^{ss}/\\!/G$ constructed earlier by the authors. The results in this paper also complement a result by Halpern-Leistner (and similar results by Ballard-Favero-Katzarkov and Donovan-Segal) that asserts the existence of a semi-orthogonal decomposition of the derived category of $X/G$ in which one of the components is the derived category of $X^{ss}/G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-09T11:53:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13A50",
      "14L24",
      "16E35"
    ],
    "keywords": [
      "semi-orthogonal decomposition",
      "derived category",
      "coherent sheaves",
      "corresponding git quotient stack",
      "finite global dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160302858S"
    }
  }
}