Multiple polylogarithms and mixed Tate motives
A. B. Goncharov
TL;DR
This paper develops a comprehensive theory of multiple polylogarithms, exploring their analytic, Hodge, and motivic aspects, and introduces the category of mixed Tate motives over number fields.
Contribution
It explicitly constructs the multiple polylogarithm Hopf algebra and defines the category of mixed Tate motives over rings of integers in number fields.
Findings
Explicit description of the multiple polylogarithm Hopf algebra
Development of the theory from analytic, Hodge, and motivic perspectives
Definition of the category of mixed Tate motives over number fields
Abstract
We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. Describe explicitly the multiple polylogarithm Hopf algebra.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Molecular spectroscopy and chirality