Motivic multiple zeta values and the block filtration

Keilthy, Adam

doi:10.1016/j.jnt.2021.10.006

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Motivic multiple zeta values and the block filtration

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Keilthy, Adam
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jnt.2021.10.006
(Publisher version)

https://doi.org/10.48550/arXiv.2006.03003
(Preprint)

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Citation

Keilthy, A. (2022). Motivic multiple zeta values and the block filtration. Journal of Number Theory, 238, 883-919. doi:10.1016/j.jnt.2021.10.006.

Cite as: https://hdl.handle.net/21.11116/0000-0009-A469-8

Abstract

We extend the block filtration, defined by Brown based on the work of
Charlton, to all motivic multiple zeta values, and study relations compatible
with this filtration. We construct a Lie algebra describing relations among
motivic multiple zeta values modulo terms of lower block degree, proving
Charlton's cyclic insertion conjecture in this structure, and showing the
existence of a `block shuffle' relation, and a previously unknown dihedral
symmetry and differential relation.