{
  "id": "1405.4625",
  "version": "v2",
  "published": "2014-05-19T07:28:17.000Z",
  "updated": "2014-06-14T09:19:35.000Z",
  "title": "Covering groups and their integral models",
  "authors": [
    "Martin H. Weissman"
  ],
  "comment": "Mistake in Section 4.2 has been fixed, leading to a much simpler argument",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Given a reductive group $\\boldsymbol{\\mathrm{G}}$ over a base scheme $S$, Brylinski and Deligne studied the central extensions of a reductive group $\\boldsymbol{\\mathrm{G}}$ by $\\boldsymbol{\\mathrm{K}}_2$, viewing both as sheaves of groups on the big Zariski site over $S$. Their work classified these extensions by three invariants, for $S$ the spectrum of a field. We expand upon their work to study \"integral models\" of such central extensions, obtaining similar results for $S$ the spectrum of a sufficiently nice ring, e.g., a DVR with finite residue field or a DVR containing a field. Milder results are obtained for $S$ the spectrum of a Dedekind domain, often conditional on Gersten's conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-14T09:19:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14L99",
      "19C09"
    ],
    "keywords": [
      "integral models",
      "covering groups",
      "central extensions",
      "reductive group",
      "finite residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4625W"
    }
  }
}