On the top-dimensional cohomology of arithmetic Chevalley groups

Let K K be a number field with ring of integers O O and let G G be a Chevalley group scheme not of type E 8 E_8 , F 4 F_4 or G 2 G_2 . We use the theory of Tits buildings and a result of Tóth on Steinberg modules to prove that H v c d ( G ( O ) ; Q ) = 0 H^{{vcd}}(G(O); Q) = 0 if O O is Euclidean.