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THE ADDITIVE DILOGARITHM

A notion of additive dilogarithm for a field k is introduced, based on the K-theory and higher Chow groups of the affine line relative to 2(0). Analogues of the K2-regulator, the polylogarithm Lie algebra, and the `-adic realization of the dilogarithm motive are discussed. The higher Chow groups of 0-cycles in this theory are identified with the Kähler differential forms Ωk. It is hoped that these results will serve as a guide in developing a theory of contravariant motivic cohomology with modulus, modelled on the generalized Jacobians of Rosenlicht and Serre.