Finiteness properties of soluble arithmetic groups over global function fields
Group Theory
2014-11-11 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.math/0212365,
title = {Finiteness properties of soluble arithmetic groups over global function fields},
author = {Kai-Uwe Bux},
journal= {arXiv preprint arXiv:math/0212365},
year = {2014}
}
Comments
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper15.abs.html