We study the action of the absolute Galois group on the pro-l completion of the fundamental group of the projective line minus zero, infinity and N-th roots of unity. The Lie algebra of the image of the Galois group is filtered by the so called depth filtration. We suggest a hypothetical description of the associated graded quotient. Using the results of our previous paper we relate it to the geometry of modular varieties for GL_m and prove it for N=1 up to the depth 3.
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