I will indicate how one can use Tits buildings to show that the "top-degree" cohomology of Sp_2n(R), the symplectic group over a number ring R, depends on number theoretic properties of R: In recent work with Himes, we proved that Sp_2n(R) has non-trivial rational cohomology in its virtual cohomological dimension if R is not a principal ideal domain. We gave a lower bound for the dimension of these cohomology groups in terms of the class number of R. This contrasts results joint with Santos-Rego-Sroka that show that the top-degree cohomology group of Sp_2n(R) is trivial if R is Euclidean. Both of these results have counterparts in the setting of SL_n(R) that were established by Church-Farb-Putman. A key ingredient in all of this is the action of these groups on associated Tits buildings.