REGULATORS ON ADDITIVE HIGHER CHOW GROUPS

Abstract

As an attempt to understand motives over k[x]/(x(m)), we define the cubical additive higher Chow groups with modulus for all dimensions extending the works of S. Bloch, H. Esnault and K. Rulling on 0-dimensional cycles. we give an explicit construction of regulator maps on the groups of I-cycles with an aid of the residue theory of A. Parshin and V. Lomadze.