Multiple zeta-values, Galois groups, and geometry of modular varieties

Details Multiple zeta-values, Galois groups, and geometry of modular varieties Multiple zeta-values, Galois groups, and geometry of modular varieties

2000-05-08

arxiv.org/abs/math/0005069v2

Mathematics

Algebraic Geometry

24 pages, 8 pictures, talk at the European Congress of Math., 2000

Scientific paper

We discuss the following two problems: 1) The properties of the multiple zeta-values and their generalizations, multiple polylogarithms at N-th roots of unity; 2) The action of the absolute Galois group on the pro-l-completion of the fundamental group of the projective line without zero, infinity, and all N-th roots of unity; and a surprising connection of these problems with the geometry and topology of modular varieties for GL_m.

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