Abstract
In this paper, we construct some maps related to the motivic Galois action on depth-graded motivic multiple zeta values. From these maps we give some short exact sequences about depth-graded motivic multiple zeta values in depth two and three. In higher depth we conjecture that there are exact sequences of the same type. We will show from three conjectures about depth-graded motivic Lie algebra we can nearly deduce the exact sequences conjectures in higher depth. At last we give a new proof of the result that the modulo \(\zeta ^{\mathfrak {m}}(2)\) version motivic double zeta values are generated by the totally odd part. We reduce the well-known conjecture that the modulo \(\zeta ^{\mathfrak {m}}(2)\) version motivic triple zeta values are generated by the totally odd part to an isomorphism conjecture in linear algebra.
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Acknowledgements
In this paper, the author wants to thank Pierre Deligne for his explanations of the author’s questions about mixed Tate motives. The author also thanks Yuancao Zhang for his help about understanding many details during the author’s study. The author also thanks Leila Schneps for her detailed explanation of a fact in her and Samuel Baumard’s paper [1]. At last, the author wants to thank his supervisor Qingchun Tian for his suggestion to choose this subject and helpful advice during the research.
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Communicated by Toby Gee.
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Li, J. The depth structure of motivic multiple zeta values. Math. Ann. 374, 179–209 (2019). https://doi.org/10.1007/s00208-018-1763-z
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DOI: https://doi.org/10.1007/s00208-018-1763-z