A criterion to determine residual coordinates of $\mathbb{A}^2$-fibrations

TL;DR

This paper introduces a criterion to identify residual variables in $ ext{A}^2$-fibrations over Noetherian domains containing the rational numbers, aiding in understanding their structure.

Contribution

It provides a new criterion for determining residual variables in $ ext{A}^2$-fibrations, advancing the analysis of their algebraic structure.

Findings

Established a criterion for residual variables in $ ext{A}^2$-fibrations

Applied the criterion to specific classes of fibrations

Enhanced understanding of the structure of $ ext{A}^2$-fibrations

Abstract

This article discusses a criterion to determine residual variables of an $\mathbb{A}^2$-fibration over a Noetherian domain containing $\mathbb{Q}$.