Abstract
Let k be a field of characteristic zero, and k[e]n := k[e]/(e ). We construct an additive dilogarithm Li2,n : B2(k[e]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[e]n has cohomology groups expressed in terms of the K-groups K·(k[e]n) as expected. Finally we compare this construction to the construction of the additive dilogarithm by Bloch and Esnault [5] defined on the complex TnQ(2)(k).
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