Periods and mixed motives
نویسنده
چکیده
We define motivic multiple polylogarithms and prove the double shuffle relations for them. We use this to study the motivic fundamental group π 1 (Gm −μN ), where μN is the group of all N -th roots of unity, and relate the structure of π 1 (Gm − μN ) to the geometry and topology of modular varieties Xm(N) := Γ1(m;N)\GLm(R)/R ∗ + ·Om for m = 1, 2, 3, 4, .... We get new results about the action of the Galois group on π (l) 1 (Gm −μN ), and about the values of multiple polylogarithms at N -th roots of unity. To prove these results we develop some tools, including the following:
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