On the Hasse Principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field

TL;DR

This paper proves the Hasse principle for the Brauer group of a one-variable purely transcendental extension over any field, extending understanding of local-global principles in algebraic geometry.

Contribution

It establishes the Hasse principle for the Brauer group in a new setting involving purely transcendental extensions over arbitrary fields.

Findings

Hasse principle holds for the Brauer group in this context

Extends known results to more general fields

Provides a foundation for further research in algebraic geometry

Abstract

In this paper we show the Hasse principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field.