Hasse principle for character group of finitely generated field over the rational number field

TL;DR

This paper proves the Hasse principle for the character group of finitely generated fields over the rationals and uses it to provide an algebraic proof of unramified class field theory for arithmetical schemes.

Contribution

It establishes the Hasse principle in this context and offers a new algebraic proof of unramified class field theory for arithmetical schemes.

Findings

Hasse principle holds for character groups of finitely generated fields over Q

Provides algebraic proof of unramified class field theory

Enhances understanding of arithmetic schemes and their class field theory

Abstract

In this paper, we show the Hasse principle for the character group of a finitely generated field over the rational number field. By applying this result, we obtain an algebraic proof of unramified class field theory of arithmetical schemes.