{
  "id": "1112.2961",
  "version": "v2",
  "published": "2011-12-13T17:08:15.000Z",
  "updated": "2012-09-18T13:02:37.000Z",
  "title": "Finiteness Properties of Chevalley Groups over the Ring of (Laurent) Polynomials over a Finite Field",
  "authors": [
    "Stefan Witzel"
  ],
  "comment": "119 pages, 10 figures, v2 with new introduction",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "In these notes we determine the finiteness length of the groups G(O_S) where G is an F_q-isotropic, connected, noncommutative, almost simple F_q-group and O_S is one of F_q[t], F_q[t^{-1}], and F_q[t,t^{-1}]. That is, k = F_q(t) and S contains one or both of the places s_0 and s_\\infty corresponding to the polynomial p(t) = t respectively to the point at infinity. The statement is that the finiteness length of G(O_S) is n-1 if S contains one of the two places and is 2n-1 if it contains both places, where n is the F_q-rank of G. For example, the group SL_3(F_q[t,t^{-1}]) is of type F_3 but not of type F_4, a fact that was previously unknown.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-18T13:02:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E42",
      "51E24",
      "57M07"
    ],
    "keywords": [
      "finiteness properties",
      "chevalley groups",
      "finite field",
      "polynomial",
      "finiteness length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 119,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.2961W"
    }
  }
}