{
  "id": "math/0612800",
  "version": "v1",
  "published": "2006-12-27T22:14:37.000Z",
  "updated": "2006-12-27T22:14:37.000Z",
  "title": "Some remarks on the derived categories of coherent sheaves on homogeneous spaces",
  "authors": [
    "Alexander Samokhin"
  ],
  "comment": "Final version. 14 pages, to appear in Journal Lond. Math. Soc",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived categories of coherent sheaves on flag varieties of classical type are generated by complete exceptional collections. Finally, we find complete exceptional collections in the derived categories of some homogeneous spaces of the symplectic groups of small rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-27T22:14:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "14M15"
    ],
    "keywords": [
      "derived categories",
      "coherent sheaves",
      "homogeneous spaces",
      "complete exceptional collections",
      "smooth base"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12800S"
    }
  }
}