Artin t-Motifs

TL;DR

This paper establishes a Tannakian duality for analytically trivial t-motifs over fields of generic characteristic, linking their Galois groups to the absolute Galois group of the base field.

Contribution

It proves a Tannakian duality for t-motifs without base field restrictions and identifies the t-motivic Galois group's components with the absolute Galois group.

Findings

Analytically trivial t-motifs satisfy Tannakian duality.

The group of components of the t-motivic Galois group equals the absolute Galois group.

No restrictions on the base field except generic characteristic.

Abstract

We show that analytically trivial t-motifs satisfy a Tannakian duality, without restrictions on the base field, save for that it be of generic characteristic. We show that the group of components of the t-motivic Galois group coincides with the absolute Galois group of the base field.