The dihedral Lie algebras and Galois symmetries of π_1^l(P^1 - 0, infinity and N-th roots of unity)

Details The dihedral Lie algebras and Galois symmetries of π_1^l(P^1 - 0, infinity and N-th roots of unity) The dihedral Lie algebras and Galois symmetries of π_1^l(P^1 - 0, infinity and N-th roots of unity)

2000-09-12

arxiv.org/abs/math/0009121v1

Mathematics

Algebraic Geometry

80 pages, extended version of the paper appeared in 1998 in K-theory archive

Scientific paper

We study the action of the Galois group on the pro-l-completion of the fundamental group of P^1 - {0, infinity and N-th roots of unity}. We describe the Lie algebra of the image of the Galois action and relate with the geometry of the modular varieties for GL_m for m = 1,2,3,... This story is the l-adic side of the motivic theory of multiple polylogarithms at roots of unity, which generalize the classical cyclotomy theory.

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