Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Finiteness properties of soluble arithmetic groups over global function fields

Kai-Uwe Bux

Geometry & Topology 8 (2004) 611–644

arXiv: math.GR/0212365

Abstract

Let G be a Chevalley group scheme and G a Borel subgroup scheme, both defined over . Let K be a global function field, S be a finite non-empty set of places over K, and OS be the corresponding S–arithmetic ring. Then, the S–arithmetic group (OS) is of type F|S|1 but not of type FP|S|. Moreover one can derive lower and upper bounds for the geometric invariants Σm((OS)). These are sharp if G has rank 1. For higher ranks, the estimates imply that normal subgroups of (OS) with abelian quotients, generically, satisfy strong finiteness conditions.

Keywords
arithmetic groups, soluble groups, finiteness properties, actions on buildings
Mathematical Subject Classification 2000
Primary: 20G30
Secondary: 20F65
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Publication
Received: 10 April 2003
Revised: 8 April 2004
Accepted: 19 December 2004
Published: 12 April 2004
Proposed: Benson Farb
Seconded: Martin Bridson, Steven Ferry
Authors
Kai-Uwe Bux
Cornell University
Department of Mathemtics
Malott Hall 310
Ithaca
New York 14853-4201
USA
http://www.kubux.net/