{
  "id": "1401.7256",
  "version": "v2",
  "published": "2014-01-28T16:58:34.000Z",
  "updated": "2014-12-20T21:23:43.000Z",
  "title": "Modular perverse sheaves on flag varieties II: Koszul duality and formality",
  "authors": [
    "Pramod N. Achar",
    "Simon Riche"
  ],
  "comment": "40 pages. v2: minor revisions",
  "categories": [
    "math.RT"
  ],
  "abstract": "Building on the theory of parity sheaves due to Juteau-Mautner-Williamson, we develop a formalism of \"mixed modular perverse sheaves\" for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a \"Koszul-type\" derived equivalence relating a given flag variety to the Langlands dual flag variety, and (2) a formality theorem for the modular derived category of a flag variety (extending a previous result of Riche-Soergel-Williamson).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-28T16:58:34.000Z",
      "comment": "38 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-20T21:23:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "koszul duality",
      "langlands dual flag variety",
      "mixed modular perverse sheaves",
      "formality theorem",
      "parity sheaves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7256A"
    }
  }
}