@inproceedings{BehrHigherFP, title={Higher finiteness properties of S-arithmetic groups in the function field case I}, author={Helmut Behr} }

It is well known that S-arithmetic subgroups of reductive algebraic groups over number fields have “all” finiteness properties (see [BS 2]). On the contrary there exist many counterexamples in the function field case. Let F be a finite extension of Fq(t), G an almost simple algebraic group of F -rank r, 0S an S-arithmetic subring of F with #S = s, rv the Fv-rank of G over the completion Fv of F for v ∈ S, and finally Γ a S-arithmetic subgroup of G(F ).