FINITENESS PROPERTIES OF CHEVALLEY GROUPS OVER F(q)[t]

Let G be a simple Chevalley group of rank n and Gamma = (G) under bar (F(q)([t]). Then the finiteness length of F shall be determined by studying the action of F on the Bruhat-Tits building X of (G) under bar (F(q)((1/t))). This is always possible provided that certain subcomplexes of t h e links of simplices in X axe spherical. As a consequence, one obtains that F is of type F(n-1) but not of type FP(n) if (G) under bar is of type A(n), B(n), C(n) or D(n) and q >= 2(2n-1).