Algebraic cycles and additive dilogarithm
Abstract
Description
For an algebraically closed field $k$ of characteristic 0, we give a cycle-theoretic description of the additive 4-term motivic exact sequence associated to the additive dilogarithm of J.-L. Cathelineau, that is the derivative of the Bloch-Wigner function, via the cubical additive higher Chow groups under one assumption. The 4-term functional equation of Cathelineau, an additive analogue of Abel's 5-term functional equation, is also discussed cycle-theoretically.
15 pages. v2: major revision. Notations made coherent. Relationship among several versions of "additive Bloch groups": 1) Cathelineau-Goncharov 2) Bloch-Esnault, and 3) the cycle-theoretic one in this paper, clarified., v3: typos, grammatical errors corrected. Final version to appear in IMRN
15 pages. v2: major revision. Notations made coherent. Relationship among several versions of "additive Bloch groups": 1) Cathelineau-Goncharov 2) Bloch-Esnault, and 3) the cycle-theoretic one in this paper, clarified., v3: typos, grammatical errors corrected. Final version to appear in IMRN