{
  "id": "0810.0794",
  "version": "v3",
  "published": "2008-10-05T01:13:58.000Z",
  "updated": "2013-01-07T18:45:23.000Z",
  "title": "Character sheaves on unipotent groups in positive characteristic: foundations",
  "authors": [
    "Mitya Boyarchenko",
    "Vladimir Drinfeld"
  ],
  "comment": "106 pages, LaTeX; to appear in Selecta Mathematica",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G gives rise to an L-packet of character sheaves on G, and that, conversely, every L-packet of character sheaves on G arises from a (non-unique) admissible pair. In the appendices we discuss two abstract category theory patterns related to the study of character sheaves. The first appendix sketches a theory of duality for monoidal categories, which generalizes the notion of a rigid monoidal category and is close in spirit to the Grothendieck-Verdier duality theory. In the second one we use a topological field theory approach to define the canonical braided monoidal structure and twist on the equivariant derived category of constructible sheaves on an algebraic group; moreover, we show that this category carries an action of the surface operad. The third appendix proves that the \"naive\" definition of the equivariant constructible derived category with respect to a unipotent algebraic group is equivalent to the \"correct\" one.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-01-07T18:45:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "character sheaves",
      "unipotent groups",
      "positive characteristic",
      "category theory patterns",
      "foundations"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 106,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0794B"
    }
  }
}