  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.
