PUB - Publikationen an der Universität Bielefeld

Let G(O(S)) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O(S)) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O(S)) established in an earlier paper is sharp in this case. The geometric analysis underlying our result determines the connectivity properties of horospheres in thick Euclidean buildings.