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Algebraic cycles and motivic generic iterated integrals

Hidekazu Furusho·Amir Jafari
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Abstract

Following the work of Gangl, Goncharov and Levin in [GGL], we will give a combinatorial framework for motivic study of iterated integrals on the affine line. We will show that under a certain genericity condition these combinatorial objects yield to elements in the motivic Hopf algebra constructed in Bloch-Kriz [BK]. It will be shown that the Hodge realization of these elements coincides with the Hodge structure induced from the fundamental torsor of path of punctured affine line.

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Hidekazu Furusho, Amir Jafari. 2005-06-18. Algebraic cycles and motivic generic iterated integrals. https://arxiv.org/abs/math/0506370

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