Untitled

Abstract

Let k be a field of characteristic zero, and let k[ε] n := k[ε]/(ε n). We construct an additive dilogarithm Li 2,n : B 2 (k[ε] n) → k ⊕(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[ε] n has cohomology groups expressed in terms of the K-groups K (•) (k[ε] n) as expected. Finally we compare this construction to the construction of the additive dilogarithm by Bloch and Esnault defined on the complex T n ‫()2(ޑ‬k). MSC2000: 11G55.