Periods and mixed motives

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

103 pages, corrected version, sections 3.5 and 10.4 added

References in corpus (3)

• Multiple polylogarithms and mixed Tate motives
• Hodge structure on the fundamental group and its application to p-adic integration
• Doubles melanges des polylogarithmes multiples aux racines de l'unit'e

Cited by in corpus (18)

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• Relationships between multiple zeta values of depths 2 and 3 and period polynomials
• Feynman integrals and periods in configuration spaces
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• Multiple zeta-motives and moduli spaces M_{0,n}
• Multizeta values: Lie algebras and periods on ${\mathfrak{M}}_{0,n}$
• Combinatorial remarks on the cyclic sum formula for multiple zeta values
• Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications
• Algebra structure of multiple zeta values in positive characteristic
• Moduli Spaces and Multiple Polylogarithm Motives
• Sum formulas for double polylogarithms with a shifting parameter and their derivatives
• On Ecalle's and Brown's polar solutions to the double shuffle equations modulo products
• Duality formula and its generalization for Schur multiple zeta functions
• Generating functions from the viewpoint of Rota-Baxter algebras
• Some examples of calculation of massless and massive Feynman integrals