{
  "id": "1911.02861",
  "version": "v1",
  "published": "2019-11-07T11:35:52.000Z",
  "updated": "2019-11-07T11:35:52.000Z",
  "title": "Etale Fundamental group of moduli of torsors under Bruhat-Tits group scheme over a curve",
  "authors": [
    "A. J. Parameswaran",
    "Yashonidhi Pandey"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\\mathcal{G}$ be a Bruhat-Tits group scheme on $X$ which is generically semi-simple and trivial. We show that the \\'etale fundamental group of the moduli stack $\\mathcal{M}_X(\\mathcal{G})$ of torsors under $\\mathcal{G}$ is isomorphic to that of the moduli stack $\\mathcal{M}_X(G)$ of principal $G$-bundles. For any smooth, noetherian and irreducible stack $\\mathcal{X}$, we show that an inclusion of an open substack $\\mathcal{X}^\\circ$, whose complement has codimension at least two, will induce an isomorphism of \\'etale fundamental group. Over $\\mathbb{C}$, we show that the open substack of regularly stable torsors in $\\mathcal{M}_X(\\mathcal{G})$ has complement of codimension at least two when $g_X \\geq 3$. As an application, we show that the moduli space $M_X(\\mathcal{G})$ of $\\mathcal{G}$-torsors is simply-connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-07T11:35:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F22",
      "14D23",
      "14D20"
    ],
    "keywords": [
      "etale fundamental group",
      "bruhat-tits group scheme",
      "moduli stack",
      "open substack",
      "smooth projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}