Geometry of the trilogarithm and the motivic Lie algebra of a field

2000/11/21 by A. B. Goncharov, Goncharov, A. B.
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0011168

This is a paper from the proceedings of Jerusalem conference on Regulators

arxiv created 2000/11/21 · openalex publication_date 2000/11/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We express the Aomoto trilogarithm explicitely via classical trilogarithm and investigate the algebraic-geometric structures behind this: different realuzations of the weight three motivic complexes. Using this results we give an explicit motivic construction of the Grassmannian 4-logarithm and Borel regulator map for K₇(C).

Related

• Polylogarithms, regulators and Arakelov motivic complexes
• Grassmannian trilogarithms
• The Grassmannian complex and Goncharov's motivic complex in weight 4
• Explicit regulator maps on polylogarithmic motivic complexes
• Motivic Integration and Logarithmic Geometry