Multiple (zeta)-Values, Galois Groups, and Geometry of Modular Varieties

摘要

The authors discuss two arithmetical problems, at first glance unrelated: (1) Theproperties of the multiple sigma-values; (2) The action of the absolute Galois group on the pro-l completion of the fundamental group. These problems are the Hodge and l-adic sites of the following one: (3) Study the Lie algebra of the image of motivic Galois group acting on the motivic fundamental group. The authors will discuss a suprising connection between these problems and geometry of the modular varieties.