{
  "id": "2303.02359",
  "version": "v1",
  "published": "2023-03-04T08:50:57.000Z",
  "updated": "2023-03-04T08:50:57.000Z",
  "title": "Hitchin map for the moduli space of $Λ$-modules in positive characteristic",
  "authors": [
    "David Alfaya",
    "Christian Pauly"
  ],
  "comment": "25 pages",
  "journal": "Journal of Algebra 634 (2023) 306-335",
  "doi": "10.1016/j.jalgebra.2023.07.012",
  "categories": [
    "math.AG"
  ],
  "abstract": "Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf $\\Lambda$ of rings of differential operators on a variety defined over a field of positive characteristic. We define the notion of $p$-curvature for $\\Lambda$-modules and the analogue of the Hitchin map on the moduli space of $\\Lambda$-modules. We show that under certain conditions this Hitchin map descends under the Frobenius map of the underlying variety and we give examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-04T08:50:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14G17"
    ],
    "keywords": [
      "moduli space",
      "positive characteristic",
      "simpsons original definition",
      "hitchin map descends",
      "frobenius map"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}