On the additive dilogarithm

Abstract

Let k be a field of characteristic zero, and let k[epsilon](n) :=k[epsilon]/(epsilon(n)). We construct an additive dilogarithm Li(2,n) : B(2) (k[epsilon](n))-> k(circle plus(n-1)), where B(2) is the Bloch group which is crucial in studying weight two motivic cohomology. We use this construction to show that the Bloch complex of k[epsilon](n) has cohomology groups expressed in terms of the K-groups K((.))(k[epsilon](n)) as expected. Finally we comparethis construction to the construction of the additive dilogarithm by Bloch and Esnault defined on the complex T(n)Q(2)(k).