The dihedral Lie algebras and Galois symmetries of \pi_1^l(P^1 - 0, infinity and N-th roots of unity)

A.B. Goncharov

The dihedral Lie algebras and Galois symmetries of \pi_1^l(P^1 - 0, infinity and N-th roots of unity)

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arxiv math/0009121 v1 pith:JWFG6GMV submitted 2000-09-12 math.AG math.NT

A.B. Goncharov This is my paper · ORCID

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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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The Hopf algebra of formal multiple polylogarithms
math.NT 2024-11 conditional novelty 6.0 of 10

A new Hopf algebra of formal multiple polylogarithms is defined for every field, with Hodge and motivic realizations, proposed as the conjectural Hopf algebra of framed mixed Tate motives.

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