Abstract

Let k be a field of characteristic zero, and let k[ε]_n := k[ε] ∕ (εⁿ). We construct an additive dilogarithm Li_2,n : B₂(k[ε]_n) → k^⊕(n−1), where B₂ 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_nQ(2)(k).

Keywords

polylogarithms, additive polylogarithms, mixed Tate motives, Hilbert's 3rd problem

Mathematical Subject Classification

Primary: 11G55

Authors