ON ADDITIVE HIGHER CHOW GROUPS OF AFFINE SCHEMES

Abstract

We show that the multivariate additive higher Chow groups of a smooth affine k-scheme Spec (R) essentially of finite type over a perfect field k of characteristic not equal 2 form a differential graded module over the big de Rham-Witt complex W-m Omega(center dot)(R). In the univariate case, we show that additive higher Chow groups of Spec (R) form a Witt-complex over R. We use these structures to prove an etale descent for multivariate additive higher Chow groups.