  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.
