AI 中文总结
本文将域的代数K-理论与多重对数关联，对数域证明Goncharov李余代数到motivic李余代数的实现映射为同构，由此得到相关猜想与ζ函数结果，还构造了Borel类非零倍的多重对数上同调类。
AI 中文摘要
本文通过一般线性群将域的代数K-理论与多重对数联系起来，聚焦数域情形，证明从Goncharov李余代数到motivic李余代数的motivic实现映射是同构，这蕴含Goncharov泛性猜想及Dedekind ζ函数特殊值的结构结果，还构造了代表Borel类非零倍的显式多重对数上同调类。
英文摘要
This paper relates algebraic K-theory of fields to polylogarithms via general linear groups. We focus on the case of number fields and prove that the motivic realisation map from the Goncharov Lie coalgebra to the motivic Lie coalgebra is an isomorphism. This implies the Goncharov universality conjecture and a structural result for special values of Dedekind zeta functions. We also construct explicit polylogarithmic cocycles representing nonzero multiples of the Borel classes.
Comments67 pages
