{
  "id": "math/0104114",
  "version": "v1",
  "published": "2001-04-10T16:31:50.000Z",
  "updated": "2001-04-10T16:31:50.000Z",
  "title": "Gluing of abelian categories and differential operators on the basic affine space",
  "authors": [
    "Roman Bezrukavnikov",
    "Alexander Braverman",
    "Leonid Positselskii"
  ],
  "comment": "14 pages",
  "journal": "Journ. Inst. Math. Jussieu 1 #4 (2002) 543-557",
  "doi": "10.1017/S1474748002000154",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "The notion of gluing of abelian categories was introduced by Kazhdan and Laumon in an attempt of another geometric construction of representations of finite Chevalley groups; the approach was later developed by Polishchuk and Braverman. We observe that this notion of gluing is a particular case of a general categorical construction (used also by Kontsevich and Rosenberg to define \"noncommutative schemes\"). We prove a conjecture of Kazhdan which says that the D-module counterpart of the Kazhdan-Laumon gluing construction produces a category equivalent to modules over the ring $\\mathcal D$ of global differential operators on the basic affine space. As an application we show that $\\mathcal D$ is Noetherian, and has finite injective dimension as a module over itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-04-10T16:31:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "basic affine space",
      "abelian categories",
      "finite chevalley groups",
      "global differential operators",
      "kazhdan-laumon gluing construction produces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......4114B"
    }
  }
}