Abstract
Let be a Chevalley group scheme and a Borel subgroup scheme, both defined over . Let be a global function field, be a finite non-empty set of places over , and be the corresponding –arithmetic ring. Then, the –arithmetic group is of type but not of type . Moreover one can derive lower and upper bounds for the geometric invariants . These are sharp if has rank . For higher ranks, the estimates imply that normal subgroups of with abelian quotients, generically, satisfy strong finiteness conditions.
Citation
Kai-Uwe Bux. "Finiteness properties of soluble arithmetic groups over global function fields." Geom. Topol. 8 (2) 611 - 644, 2004. https://doi.org/10.2140/gt.2004.8.611
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