{
  "id": "1102.2820",
  "version": "v1",
  "published": "2011-02-14T16:27:27.000Z",
  "updated": "2011-02-14T16:27:27.000Z",
  "title": "Koszul duality and semisimplicity of Frobenius",
  "authors": [
    "Pramod N. Achar",
    "Simon Riche"
  ],
  "comment": "76 pages",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "A fundamental result of Beilinson-Ginzburg-Soergel states that on flag varieties and related spaces, a certain modified version of the category of l-adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated analogue. In particular, we show that these functors preserve semisimplicity of the Frobenius action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-14T16:27:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "koszul duality",
      "functors preserve semisimplicity",
      "common sheaf functors",
      "l-adic perverse sheaves",
      "beilinson-ginzburg-soergel states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 76,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.2820A"
    }
  }
}