The motivic fundamental group of the punctured projective line

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.