{
  "id": "math/0204047",
  "version": "v2",
  "published": "2002-04-03T12:09:20.000Z",
  "updated": "2002-11-27T04:49:15.000Z",
  "title": "Representability of $GL_E$",
  "authors": [
    "Nitin Nitsure"
  ],
  "comment": "3 pages, LaTeX",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $S$ be a noetherian scheme, and let $E$ be a coherent sheaf on it. We define a group-valued contravariant functor $GL_E$ on $S$-schemes by associating to any $S$-scheme $T$ the group $GL_E(T)$ of all linear automorphisms of the pullback of $E$ to $T$. This functor is clearly a sheaf in the fpqc topology. We prove that $GL_E$ is representable by a group-scheme over $S$ if and only if the sheaf $E$ is locally free.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-27T04:49:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L15"
    ],
    "keywords": [
      "representability",
      "fpqc topology",
      "coherent sheaf",
      "noetherian scheme",
      "linear automorphisms"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......4047N"
    }
  }
}