The cyclotomic Grothendieck-Teichm\"{u}ller group and the motivic Galois group

TL;DR

This paper proves that the level 2 cyclotomic Grothendieck-Teichmüller group coincides with the motivic Galois group of mixed Tate motives over b[1/2], establishing a deep connection between these algebraic structures.

Contribution

It demonstrates the equivalence of the level 2 cyclotomic Grothendieck-Teichmüller group and the motivic Galois group for mixed Tate motives over b[1/2], clarifying their relationship.

Findings

Level 2 cyclotomic GT group equals motivic Galois group

Connection between algebraic and motivic structures established

Advances understanding of mixed Tate motives over b[1/2]

Abstract

We show that the level 2 case of the cyclotomic Grothendieck-Teichm\"{u}ller groups introduced by Enriquez coincides with the motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$.