{
  "id": "math/0212365",
  "version": "v2",
  "published": "2002-12-29T01:34:59.000Z",
  "updated": "2004-04-21T20:16:32.000Z",
  "title": "Finiteness properties of soluble arithmetic groups over global function fields",
  "authors": [
    "Kai-Uwe Bux"
  ],
  "comment": "Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper15.abs.html",
  "journal": "Geom. Topol. 8(2004) 611-644",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "Let G be a Chevalley group scheme and B<=G a Borel subgroup scheme, both defined over Z. Let K be a global function field, S be a finite non-empty set of places over K, and O_S be the corresponding S-arithmetic ring. Then, the S-arithmetic group B(O_S) is of type F_{|S|-1} but not of type FP_{|S|}. Moreover one can derive lower and upper bounds for the geometric invariants \\Sigma^m(B(O_S)). These are sharp if G has rank 1. For higher ranks, the estimates imply that normal subgroups of B(O_S) with abelian quotients, generically, satisfy strong finiteness conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-21T20:16:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G30",
      "20F65"
    ],
    "keywords": [
      "global function field",
      "soluble arithmetic groups",
      "finiteness properties",
      "satisfy strong finiteness conditions",
      "chevalley group scheme"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}