{
  "id": "1206.2764",
  "version": "v1",
  "published": "2012-06-13T10:50:21.000Z",
  "updated": "2012-06-13T10:50:21.000Z",
  "title": "A characterization of categories of coherent sheaves of certain algebraic stacks",
  "authors": [
    "Daniel Schäppi"
  ],
  "comment": "64 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.CT"
  ],
  "abstract": "Under certain conditions, a scheme can be reconstructed from its category of quasi-coherent sheaves. The Tannakian reconstruction theorem provides another example where a geometric object can be reconstructed from an associated category, in this case the category of its finite dimensional representations. Lurie's result that the pseudofunctor which sends a geometric stack to its category of quasi-coherent sheaves is fully faithful provides a conceptual explanation for why this works. In this paper we prove a generalized Tannakian recognition theorem, in order to characterize a part of the image of the extension of the above pseudofunctor to algebraic stacks in the sense of Naumann. This allows us to further investigate a conjecture by Richard Pink about categories of filtered modules, which were defined by Fontaine and Laffaille to construct p-adic Galois representations. In order to do this we give a new characterization of Adams Hopf algebroids, which also allows us to answer a question posed by Mark Hovey.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-13T10:50:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A20",
      "16T05",
      "18D20"
    ],
    "keywords": [
      "algebraic stacks",
      "characterization",
      "quasi-coherent sheaves",
      "construct p-adic galois representations",
      "finite dimensional representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.2764S"
    }
  }
}