Locally nilpotent derivations on $\mathbb{A}^2$-fibrations with $\mathbb{A}^1$-fibration kernels

TL;DR

This paper characterizes locally nilpotent derivations on certain algebraic fibrations over Noetherian domains with rational numbers, focusing on cases where the kernel is an 1-fibration, advancing understanding of algebraic derivations.

Contribution

It provides a new characterization of locally nilpotent derivations on 2-fibrations with 1-fibration kernels over Noetherian domains containing 4.

Findings

Characterization of locally nilpotent derivations established

Kernel isomorphic to an 1-fibration identified

Applicable over Noetherian domains containing 4

Abstract

In this paper, we give a characterization of locally nilpotent derivations on $\mathbb{A}^2$-fibrations over Noetherian domains containing $\mathbb{Q}$ having kernel isomorphic to an $\mathbb{A}^1$-fibration.