Moduli spaces and multiple polylogarithm motives
Copyright policy )Moduli spaces and multiple polylogarithm motives
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 $\mathcal{\bar{M}}_{0,n}$ of $n$-pointed stable curves of genus 0, and prove that the cohomology of the pair $(\mathcal{\bar{M}}_{0,n}-A,B-B\cap A)$ 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.
24 pages, 2 figures, to appear in Adv.in Math
- Oklahoma State University–Stillwater United States
Mathematics(all), Mathematics - Number Theory, Framed Hodge–Tate structures, mixed Tate motives, Galois theory, Multiple polylogarithms, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Higher logarithm functions, Mathematics - Algebraic Geometry, Algebraic moduli problems, moduli of vector bundles, framed Hodge-Tate structures, FOS: Mathematics, moduli spaces, Mixed Tate motives, Number Theory (math.NT), multiple polylogarithms, Algebraic Geometry (math.AG), Polylogarithms and relations with \(K\)-theory, Moduli spaces
Mathematics(all), Mathematics - Number Theory, Framed Hodge–Tate structures, mixed Tate motives, Galois theory, Multiple polylogarithms, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Higher logarithm functions, Mathematics - Algebraic Geometry, Algebraic moduli problems, moduli of vector bundles, framed Hodge-Tate structures, FOS: Mathematics, moduli spaces, Mixed Tate motives, Number Theory (math.NT), multiple polylogarithms, Algebraic Geometry (math.AG), Polylogarithms and relations with \(K\)-theory, Moduli spaces
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