Vol. 3, No. 1, 2009

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On the additive dilogarithm

Sinan Ünver

Vol. 3 (2009), No. 1, 1–34

Let k be a field of characteristic zero, and let k[ε]n := k[ε](εn). We construct an additive dilogarithm Li2,n : B2(k[ε]n) k(n1), 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 Tn(2)(k).

polylogarithms, additive polylogarithms, mixed Tate motives, Hilbert's 3rd problem
Mathematical Subject Classification 2000
Primary: 11G55
Received: 14 September 2007
Revised: 1 November 2008
Accepted: 11 November 2008
Published: 1 February 2009
Sinan Ünver
Koç University
Department of Mathematics
Rumelifeneri Yolu
34450 Sarıyer-İstanbul