{
  "id": "1910.03377",
  "version": "v1",
  "published": "2019-10-08T13:09:58.000Z",
  "updated": "2019-10-08T13:09:58.000Z",
  "title": "Perverse $\\mathbb{F}_p$ sheaves on the affine Grassmannian",
  "authors": [
    "Robert Cass"
  ],
  "comment": "51 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a reductive group over an algebraically closed field of characteristic $p > 0$ we construct the abelian category of perverse $\\mathbb{F}_p$ sheaves on the affine Grassmannian that are equivariant with respect to the action of the positive loop group. We show this is a symmetric monoidal category, and then we apply a Tannakian formalism to show this category is equivalent to the category of representations of a certain affine monoid scheme. We also show that our work provides a geometrization of the inverse of the mod $p$ Satake isomorphism. Along the way we prove that affine Schubert varieties are globally $F$-regular and we apply Frobenius splitting techniques to the theory of perverse $\\mathbb{F}_p$ sheaves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-08T13:09:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "14F10",
      "14F20"
    ],
    "keywords": [
      "affine grassmannian",
      "symmetric monoidal category",
      "affine monoid scheme",
      "affine schubert varieties",
      "abelian category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}