The aim of this talk is to discuss a vanishing result for the top-dimensional rational cohomology of arithmetic Chevalley groups such as SL_n(Z). I will introduce this class of groups, which can be thought of as the algebraic counterpart of semisimple Lie groups, together with the Tits building, a geometric object on which they act. Via Borel?Serre duality, understanding the top-dimensional rational cohomology reduces to a combinatorial question about the homology of the building. We will see that this cohomology vanishes for G(O), where G is any semisimple Chevalley group with irreducible root system and O is a Euclidean ring of integers. This completes previous work of Tóth and of Brück, Santos Rego and Sroka.