Geometric Class Field Theory

TL;DR

This paper presents a geometric proof of global class field theory, extending Deligne's unramified case to include tamely ramified cases through generalization of key concepts.

Contribution

It provides a purely geometric proof of global class field theory, including both unramified and tamely ramified cases, based on Deligne's approach.

Findings

Proof of unramified class field theory using geometric methods

Extension of proof to tamely ramified case

Clarification of geometric objects involved in class field theory

Abstract

In this paper we prove global class field theory using a purely geometric result. We first write in detail Deligne's proof to the unramified case of class field theory, including defining the required objects for the proof. Then we generalize the notions appearing in the proof to prove also the tamely ramified case relying on the unramified one.