Explicit regulator maps on polylogarithmic motivic complexes

Details Explicit regulator maps on polylogarithmic motivic complexes Explicit regulator maps on polylogarithmic motivic complexes

2000-03-15

arxiv.org/abs/math/0003086v1

Mathematics

Algebraic Geometry

30 pages, 1 figure

Scientific paper

We define a regulator map from the weight n polylogarithmic motivic complex to the weight n Deligne complex of an algebraic variety X. The regulator map is constructed explicitly via the classical polylogarithms with some funny combinations of Bernoulli numbers as coefficients. This leads to conjectures on special values of L-functions at s=n which reduce to Zagier's conjecture when X is of dimension zero over Q. The cone of this map, shifted by one, should be called the Arakelov motivic complex of X. Its last cohomology group is identified with a group of codimension n Arakelov cycles on X.

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