{
  "id": "1104.4828",
  "version": "v1",
  "published": "2011-04-26T00:34:16.000Z",
  "updated": "2011-04-26T00:34:16.000Z",
  "title": "The moduli stack of $G$-bundles",
  "authors": [
    "Jonathan Wang"
  ],
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "In this paper, we give an expository account of the geometric properties of the moduli stack of $G$-bundles. For $G$ an algebraic group over a base field and $X \\to S$ a flat, finitely presented, projective morphism of schemes, we give a complete proof that the moduli stack $Bun_G$ is an algebraic stack locally of finite presentation over $S$ with schematic, affine diagonal. In the process, we prove some properties of $BG$ and Hom stacks. We then define a level structure on $Bun_G$ to provide alternative presentations of quasi-compact open substacks. Finally, we prove that $Bun_G$ is smooth over $S$ if $G$ is smooth and $X \\to S$ is a relative curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-26T00:34:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli stack",
      "quasi-compact open substacks",
      "algebraic group",
      "base field",
      "complete proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.4828W"
    }
  }
}