{
  "id": "0802.1260",
  "version": "v1",
  "published": "2008-02-11T09:16:07.000Z",
  "updated": "2008-02-11T09:16:07.000Z",
  "title": "A characterization of the overcoherence",
  "authors": [
    "Daniel Caro"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $\\mathcal{P}$ be a proper smooth formal $\\mathcal{V}$-scheme, $X$ a closed subscheme of the special fiber of $\\mathcal{P}$, $\\mathcal{E} \\in F\\text{-}D ^\\mathrm{b}_\\mathrm{coh} (\\D ^\\dag_{\\mathcal{P},\\mathbb{Q}})$ with support in $X$. We check that $\\mathcal{E}$ is $\\D ^\\dag _{\\mathcal{P},\\mathbb{Q}}$-overcoherent if and only if, for any morphism $f : \\mathcal{P}' \\to \\mathcal{P}$ of smooth formal $\\mathcal{V}$-schemes, $f ^! (\\mathcal{E}) $ is $\\D ^\\dag_{\\mathcal{P}', \\mathbb{Q}}$-coherent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-02-11T09:16:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F30"
    ],
    "keywords": [
      "characterization",
      "overcoherence",
      "proper smooth formal",
      "special fiber"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.1260C"
    }
  }
}