The base change of the monodromy group for geometric Tannakian pairs

TL;DR

This paper proves that the formation of the monodromy group of a D-module commutes with ground field extension in any characteristic, generalizing Gabber's result for separable extensions.

Contribution

It extends Gabber's result by showing the monodromy group formation commutes with ground field extension in all characteristics.

Findings

Monodromy group formation commutes with ground field extension in any characteristic.

Generalization of Gabber's result beyond separable extensions.

Applicable to geometric Tannakian pairs.

Abstract

We prove that in any characteristic the formation of the monodromy group of a $\mathscr{D}$-module commutes with the extension of the ground field, extending a result of Gabber for separable extensions.