2000/03/15 by A. B. Goncharov, Goncharov, A. B. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT) #math.AG #math.KT #math.NT
paper · pdf · doi:10.48550/arxiv.math/0003086
30 pages, 1 figure
arxiv created 2000/03/15 · openalex publication_date 2000/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.