Motivic Cohomology

By definition, NK_0(R) is K_0(R[t]) modulo K_0(R). We give a formula for this group when R is of finite type over a field of characteristic zero. The group is bigraded and determined by its typical pieces, which are the cdh cohomology groups H^p(R,\Omega^p). We also partially answer a question of Bass by proving that if NK_0(R) and NK_n(R) vanish for all negative n then K_0(R)=K_0(R[t,u,v,...,z]). This is joint work with Haesemeyer and Cortinas.