Non-Abelian Class Field Theory for Riemann Surfaces

TL;DR

This paper advances non-abelian class field theory for Riemann surfaces by establishing a micro reciprocity law, completing Weil's program in this area.

Contribution

It introduces a micro reciprocity law that completes Weil's non-abelian class field theory for Riemann surfaces, a significant extension of classical results.

Findings

Establishment of a micro reciprocity law

Completion of Weil's program for non-abelian class field theory

Advancement in understanding Riemann surface symmetries

Abstract

In this paper, using what we call a micro reciprocity law, we complete Weil's program for non-abelian class field theory of Riemann surfaces.