{
  "id": "1801.04784",
  "version": "v1",
  "published": "2018-01-15T13:08:02.000Z",
  "updated": "2018-01-15T13:08:02.000Z",
  "title": "Triviality properties of principal bundles on singular curves-II",
  "authors": [
    "Prakash Belkale",
    "Najmuddin Fakhruddin"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "For $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\\to S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D \\subset X$. We show, by constructing explicit examples, that the obstruction is nontrivial if $G$ is not simply connected but it can be made to vanish, if $S$ is the spectrum of a dvr (and some other hypotheses), by a faithfully flat base change. The vanishing of this obstruction is shown to be a sufficient condition for etale local triviality if $S$ is a smooth curve, and the singular locus of $X-D$ is finite over $S$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-15T13:08:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14H60",
      "14H20"
    ],
    "keywords": [
      "triviality properties",
      "principal bundles",
      "singular curves-ii",
      "split semi-simple group scheme",
      "etale local triviality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}