{
  "id": "1506.07828",
  "version": "v1",
  "published": "2015-06-25T17:28:11.000Z",
  "updated": "2015-06-25T17:28:11.000Z",
  "title": "Principal bundles under a reductive group",
  "authors": [
    "Peter O'Sullivan"
  ],
  "comment": "111 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $k$ be a field of characteristic $0$. We consider principal bundles over a $k$-scheme with reductive structure group (not necessarily of finite type). It is showm in particular that for $k$ algebraically closed there exists on any complete connected $k$-scheme a universal such bundle. As a consequence, an explicit description of principal bundles with reductive structure group over curves of genus $0$ or $1$ is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T17:28:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal bundles",
      "reductive group",
      "reductive structure group",
      "finite type",
      "explicit description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 111,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}