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Periods and mixed motives

A. B. Goncharov
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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

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A. B. Goncharov. 2002-05-27. Periods and mixed motives. https://arxiv.org/abs/math/0202154

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