2006/10/23 by Qingxue Wang, Wang, Qingxue
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Analytic and geometric function theory #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0610670
24 pages, 2 figures, to appear in Adv.in Math
arxiv created 2006/10/23 · openalex publication_date 2006/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors A and B in the moduli spaces \mathcalM0,n of n-pointed stable curves of genus 0, and prove that the cohomology of the pair (\mathcalM0,n-A,B-B∩ A) is a framed mixed Tate motive whose period is that integral. It generalizes the results of A. Goncharov and Yu. Manin for multiple zeta values. Then we apply our construction to the dilogarithm and calculate the period matrix which turns out to be same with the canonical one of Deligne.