{
  "id": "1605.08997",
  "version": "v1",
  "published": "2016-05-29T12:21:48.000Z",
  "updated": "2016-05-29T12:21:48.000Z",
  "title": "Harder-Narasimhan stacks for principal bundles in higher dimensions",
  "authors": [
    "Sudarshan Gurjar",
    "Nitin Nitsure"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $G$ be a connected split reductive group over a field $k$ of arbitrary characteristic, chosen suitably. Let $X\\to S$ be a smooth projective morphism of locally noetherian $k$-schemes, with geometrically connected fibers. We show that for each Harder-Narasimhan type $\\tau$ for principal $G$-bundles, all pairs consisting of a principal $G$-bundle on a fiber of $X\\to S$ together with a given canonical reduction of HN-type $\\tau$ form an Artin algebraic stack $Bun_{X/S}^{\\tau}(G)$ over $S$. Moreover, the forgetful $1$-morphism $Bun_{X/S}^{\\tau}(G) \\to Bun_{X/S}(G)$ to the stack of all principal $G$-bundles on fibers of $X\\to S$ is a schematic morphism, which is of finite type, separated and injective on points. The notion of a relative canonical reduction that we use was defined earlier in arXiv:1505.02236, where we showed that a stronger result holds in characteristic zero, namely, the $1$-morphisms $Bun_{X/S}^{\\tau}(G) \\to Bun_{X/S}(G)$ are locally closed imbeddings which stratify $Bun_{X/S}(G)$ as $\\tau$ varies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-29T12:21:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D20",
      "14D23"
    ],
    "keywords": [
      "principal bundles",
      "higher dimensions",
      "harder-narasimhan stacks",
      "canonical reduction",
      "stronger result holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}