The motivic fundamental group of the punctured projective line
Bertrand J. Guillou

TL;DR
This paper constructs a motivic version of the fundamental group of the thrice-punctured projective line using mixed Tate motives and motivic cohomology, revealing deep algebraic structures.
Contribution
It introduces a novel construction linking the fundamental group to mixed Tate motives via Massey products in motivic cohomology.
Findings
Establishes a motivic fundamental group object for the punctured projective line.
Connects Massey products of Steinberg symbols to motivic fundamental groups.
Provides a new perspective on the algebraic structure of fundamental groups in motivic cohomology.
Abstract
We describe a construction of an object associated to the fundamental group of the projective line minus three points in the Bloch-Kriz category of mixed Tate motives. This description involves Massey products of Steinberg symbols in the motivic cohomology of the ground field.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra
