Non-abelian class field theory and higher dimensional noncommutative tori

TL;DR

This paper explores the connection between Drinfeld modules and higher-dimensional noncommutative tori to develop a non-abelian class field theory, providing explicit Galois extension generators.

Contribution

It introduces a novel non-abelian class field theory linking noncommutative geometry and number theory, with explicit Galois extension generators.

Findings

Established a relation between Drinfeld modules and noncommutative tori

Developed a non-abelian class field theory framework

Constructed explicit generators of Galois extensions

Abstract

We study a relation between the Drinfeld modules and the even dimensional noncommutative tori. A non-abelian class field theory is developed based on this relation. Explicit generators of the Galois extensions are constructed.