Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motivic fundamental group of ${\Bbb G}_m-\mu_N$ and modular manifolds   We investigate geometric and combinatorial aspects of the mysterious
relationship between the action of the motivic Galois group on the motivic
fundamental group of the projective line punctured at zero, infinity, and N-th
roots of unity, and the geometry of modular manifolds for the congruence
subgroup Y(m;N) of GL(m,Z) fixing (0, ... , 0, 1) modulo N. To achieve this, we
consider a canonical collection of elements in the image of the motivic Galois
Lie algebra, spanning it over Q. These elements are the motivic correlators at
N-th roots of unity. We assign to them chains in the complex computing
cohomology of certain local systems on the space Y(m;N). Their geometric
properties reflect, in a mysterious way, properties of motivic correlators.
This construction allows to establish the relationship with high precision for
m up to 4. The m=2, 3 cases were investigated by the author before in the Hodge
and the Galois set-up.

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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph