Groupes fondamentaux motiviques de Tate mixte

TL;DR

This paper defines the category of mixed Tate motives over S-integers of a number field and studies the motivic fundamental group of certain algebraic varieties, including the punctured projective line.

Contribution

It introduces the concept of mixed Tate motives over S-integers and constructs the unipotent motivic fundamental group for specific algebraic varieties.

Findings

Defined the category of mixed Tate motives over S-integers.

Constructed the unipotent motivic fundamental group of the punctured projective line.

Applied the theory to analyze the motivic fundamental group of the projective line minus points.

Abstract

We define the category of mixed Tate motives over the ring of S-integers of a number field. We define the motivic fundamental group (made unipotent) of a unirational variety over a number field. We apply this to the study of the motivic fundamental group of the projective line punctured at zero, infinity and all N-th roots of unity.