Periods and mixed motives

2002/02/17 by A. B. Goncharov, Goncharov, A. B. · 3 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0202154

103 pages, corrected version, sections 3.5 and 10.4 added

openalex publication_date 2002/02/17 · arxiv created 2002/05/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group of the multiplicative group - N-th roots of unity and relate it to geometry of modular varieties. In particular we get new information about the actionof the Galois group on the pro-l completion of the above fundamental group. This paper is the second part of "Multiple polylogarithms and mixed Tate motives" math.AG/0103059

Citations

• Multiple polylogarithms and mixed Tate motives

Cited by

• Relationships between multiple zeta values of depths 2 and 3 and period polynomials
• Algebra structure of multiple zeta values in positive characteristic
• Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications

Related

• Polylogarithm Variations and Motivic Extensions of ℚ by ℚ(m)
• Multiple Modular Values and the relative completion of the fundamental group of M_1,1
• Multiple zeta-values, Galois groups, and geometry of modular varieties
• The motivic Galois group for a double zeta value
• Multiple polylogarithms and mixed Tate motives