{
  "id": "1810.11845",
  "version": "v1",
  "published": "2018-10-28T17:57:03.000Z",
  "updated": "2018-10-28T17:57:03.000Z",
  "title": "Moduli of rank 1 isocrystals",
  "authors": [
    "Efstathia Katsigianni"
  ],
  "comment": "22 pages, Comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article we express the set of rank 1 isocrystals on a proper curve as a subset of the de Rham moduli space, defined by Simpson and Langer. Using results from the theory of Berkovich spaces, we compare the $\\ell$-adic cohomology of this subspace with the $\\ell$-adic cohomology of the whole moduli space. This confirms a conjecture of Deligne in the rank 1 case and explains one of his examples in this case from the point of view of isocrystals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-28T17:57:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "isocrystals",
      "adic cohomology",
      "rham moduli space",
      "berkovich spaces",
      "proper curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}