An isomorphism of motivic Galois groups

TL;DR

This paper demonstrates that two major approaches to the theory of mixed motives in characteristic 0, Nori's and Voevodsky's, have canonically isomorphic motivic Galois groups, suggesting their fundamental equivalence.

Contribution

It proves the canonical isomorphism between the motivic Galois groups arising from Nori's and Voevodsky's frameworks, linking two major theories of mixed motives.

Findings

Motivic Galois groups from Nori and Voevodsky are canonically isomorphic.

Supports the conjecture that different approaches to mixed motives are fundamentally connected.

Provides evidence towards unifying the theory of mixed motives in characteristic 0.

Abstract

In characteristic 0 there are essentially two approaches to the conjectural theory of mixed motives, one due to Nori and the other one due to, independently, Hanamura, Levine, and Voevodsky. Although these approaches are apriori quite different it is expected that ultimately they can be reduced to one another. In this article we provide some evidence for this belief by proving that their associated motivic Galois groups are canonically isomorphic.