Functional equations of the dilogarithm in motivic cohomology

Details Functional equations of the dilogarithm in motivic cohomology Functional equations of the dilogarithm in motivic cohomology

2007-12-24

arxiv.org/abs/0712.3987v4

Journal of Number Theory 129 (2009) pp. 2346-2368

Mathematics

Number Theory

21 pages, no figures; accepted for publication in the Journal of Number Theory

Scientific paper

10.1016/j.jnt.2009.04.009

We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.

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