{
  "id": "1305.1684",
  "version": "v4",
  "published": "2013-05-08T00:07:34.000Z",
  "updated": "2015-09-17T22:26:03.000Z",
  "title": "Parity sheaves on the affine Grassmannian and the Mirković-Vilonen conjecture",
  "authors": [
    "Pramod N. Achar",
    "Laura Rider"
  ],
  "comment": "27 pages. v4: added details to Section 2 and an appendix on sheaf functors on non-locally compact spaces",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove the Mirkovi\\'c-Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers. (Juteau has exhibited counterexamples when p is a bad prime.) The main idea is to convert this topological question into an algebraic question about perverse-coherent sheaves on the dual nilpotent cone using the Juteau-Mautner-Williamson theory of parity sheaves.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-03T11:44:42.000Z",
      "comment": "22 pages. v3: corrected a mistake in Section 5",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-09-17T22:26:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E57",
      "14F05"
    ],
    "keywords": [
      "parity sheaves",
      "affine grassmannian",
      "mirković-vilonen conjecture",
      "integral local intersection cohomology groups",
      "dual nilpotent cone"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.1684A"
    }
  }
}