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

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.