Adelic Openness for Drinfeld Modules in Special Characteristic

TL;DR

This paper investigates the adelic Galois representations associated with Drinfeld modules in special characteristic, analyzing their images and the structure of the geometric Galois group.

Contribution

It provides a detailed description of the adelic Galois representation images for Drinfeld modules in special characteristic, extending understanding of their Galois symmetry.

Findings

Determined the image of the geometric Galois group up to commensurability.

Analyzed the adelic Galois representations at all places except p0 and infinity.

Extended the theory of Galois representations for Drinfeld modules in special characteristic.

Abstract

For any Drinfeld module of special characteristic p0 over a finitely generated field, we study the associated adelic Galois representation at all places different from p0 and \infty, and determine the image of the geometric Galois group up to commensurability.