{
  "id": "1009.4055",
  "version": "v1",
  "published": "2010-09-21T11:03:42.000Z",
  "updated": "2010-09-21T11:03:42.000Z",
  "title": "A short note on vector bundles on curves",
  "authors": [
    "Martin Kreidl"
  ],
  "comment": "5 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed closed point. In order to establish this correspondence, they have to show that descent for vector bundles holds in a situation which is not a classical fpqc-descent situation. They prove this as a consequence of an abstract descent lemma. It turns out, however, that one can avoid this descent lemma by using a simple approximation-argument, which leads to a more direct prove of the above mentioned correspondence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-21T11:03:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short note",
      "abstract descent lemma",
      "vector bundles holds",
      "correspondence",
      "classical fpqc-descent situation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.4055K"
    }
  }
}