{
  "id": "1201.0741",
  "version": "v2",
  "published": "2012-01-03T20:21:11.000Z",
  "updated": "2015-10-27T15:52:32.000Z",
  "title": "Moduli of flat connections in positive characteristic",
  "authors": [
    "Michael Groechenig"
  ],
  "comment": "51 pages, exposition improved, curves are allowed to acquire orbifold points in new version (except for section 4)",
  "categories": [
    "math.AG"
  ],
  "abstract": "Exploiting the description of rings of differential operators as Azumaya algebras on cotangent bundles, we show that the moduli stack of flat connections on a curve (allowed to acquire orbifold points) defined over an algebraically closed field of positive characteristic is \\'etale locally equivalent to a moduli stack of Higgs bundles over the Hitchin base. We then study the interplay with stability and generalize a result of Laszlo-Pauly, concerning properness of the Hitchin map. Using Arinkin's autoduality of compactified Jacobians we extend the main result of Bezrukavnikov-Braverman, the Langlands correspondence for D-modules in positive characteristic for smooth spectral curves, to the locus of integral spectral curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-03T20:21:11.000Z",
      "abstract": "Exploiting the description of rings of differential operators as Azumaya algebras on cotangent bundles, we show that the moduli stack of flat connections on a curve defined over an algebraically closed field of positive characteristic is \\'etale locally equivalent to a moduli stack of Higgs bundles over the Hitchin base. We then study the interplay with stability and generalize a result of Laszlo-Pauly, concerning properness of the Hitchin map. Using Arinkin's autoduality of compactified Jacobians we extend the main result of Bezrukavnikov-Braverman, the Langlands correspondence for D-modules in positive characteristic for smooth spectral curves, to the locus of integral spectral curves.",
      "comment": "34 pages, comments appreciated",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-10-27T15:52:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive characteristic",
      "flat connections",
      "moduli stack",
      "integral spectral curves",
      "smooth spectral curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.0741G"
    }
  }
}