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- W4288090164 abstract "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." @default.
- W4288090164 created "2022-07-28" @default.
- W4288090164 creator A5055891802 @default.
- W4288090164 date "2019-10-22" @default.
- W4288090164 modified "2023-10-18" @default.
- W4288090164 title "Motivic fundamental group of ${Bbb G}_m-mu_N$ and modular manifolds" @default.
- W4288090164 doi "https://doi.org/10.48550/arxiv.1910.10321" @default.
- W4288090164 hasPublicationYear "2019" @default.
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