Blow-ups and the class field theory for curves

TL;DR

This paper presents a new proof of the geometric class field theory for curves by utilizing blow-ups of symmetric products, offering an alternative approach to understanding the theory.

Contribution

It introduces a novel proof method for the geometric class field theory for curves using blow-ups of symmetric products.

Findings

Provides an alternative proof of the geometric class field theory for curves.

Utilizes blow-ups of symmetric products to establish the theory.

Enhances understanding of the relationship between blow-ups and class field theory.

Abstract

We propose another proof of the geometric class field theory for curves by considering blow-ups of symmetric products of curves.