发表机构
Université de Strasbourg（斯特拉斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究五点有理曲线模空间上迭代Kummer扩张的上同调，通过二维收缩构造比较Betti表示，得到五角星关系，并证明其与五边形方程等价，进而蕴含shuffle关系。
AI 中文摘要
我们继续研究[ arXiv:2609.19341, arXiv:2609.21356 ]，在五点有理曲线模空间上研究迭代Kummer扩张的上同调。一个二维收缩构造比较了其五个遗忘投影得到的Betti表示。相应的Hodge缺陷给出五角星关系，即Drinfeld结合子系数之间的二次关系，在群相似性、归一化和反转条件下等价于五边形方程。在反转和纯幂系数消失条件下，这些关系蕴含了shuffle和正则化双shuffle，其Hodge实现通过卷积特化恢复。
英文摘要
We study the cohomology of iterated Kummer extensions on the moduli space of five-pointed rational curves, continuing [arXiv:2609.19341, arXiv:2609.21356]. A two-dimensional shrinking construction compares the Betti presentations obtained from its five forgetful projections. The corresponding Hodge defects give pentagram relations, quadratic relations between coefficients of the Drinfeld associator, which are equivalent to the pentagon equation under group-likeness, normalization, and reversal. Under reversal and vanishing of pure-power coefficients, the relations imply shuffle and regularized double shuffle, whose Hodge realization is recovered by a convolution specialization.
Comments46 pages
