Depth-graded motivic Lie algebra

TL;DR

This paper explores the structure of depth-graded motivic Lie algebras in the context of mixed Tate motives over Z, linking conjectures to deepen understanding of their algebraic properties.

Contribution

It proposes a method to analyze the depth-graded motivic Lie subalgebra structure using an isomorphism conjecture, connecting it to existing conjectures in the field.

Findings

Deduction of the F. Brown matrix conjecture from the isomorphism conjecture

Connection established between the isomorphism conjecture and the non-degenerated conjecture

Enhanced understanding of the structure of depth-graded motivic Lie subalgebras

Abstract

Consider the neutral Tannakian category mixed Tate motives over Z, in this paper we suggest a way to understand the structure of depth-graded motivic Lie subalgebra generated by the depth one part. We will show that from an isomorphism conjecture proposed by K. Tasaka we can deduce the F. Brown matrix conjecture and the non-degenerated conjecture about depth-graded motivic Lie subalgebra generated by the depth one part.