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Double shuffle relations via the Hodge defect
Abstract
We interpret the convolution constructions of [arXiv:2604.26357] in Hodge-theoretic terms, extending the Hodge defect calculation of [arXiv:2609.19341]. For Hodge--Tate modules on ℂ* smooth outside $1$, the defect is the action of an element of the Deligne--Terasoma transport algebra expressed through the Drinfeld associator. For convolutions of iterated Kummer extensions, comparison of mixed Hodge structures produces a beta factor and yields the regularized double shuffle relations.
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BibTeX
@misc{markarian2026double,
title = {{Double shuffle relations via the Hodge defect}},
author = {Nikita Markarian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21356},
eprint = {2609.21356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21356},
}
RIS
TY - UNPB
TI - Double shuffle relations via the Hodge defect
AU - Nikita Markarian
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21356
UR - https://arxiv.org/abs/2609.21356
AB - We interpret the convolution constructions of [arXiv:2604.26357] in Hodge-theoretic terms, extending the Hodge defect calculation of [arXiv:2609.19341]. For Hodge--Tate modules on ℂ^* smooth outside $1$, the defect is the action of an element of the Deligne--Terasoma transport algebra expressed through the Drinfeld associator. For convolutions of iterated Kummer extensions, comparison of mixed Hodge structures produces a beta factor and yields the regularized double shuffle relations.
ER -