Volume 8, issue 2 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29, 1 issue Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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
References
Forward citations
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/