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arXiv · 2002.02128

A Note on Residual Variables of an Affine Fibration

Prosenjit Das·Amartya K. Dutta
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Abstract

In a recent paper [El 13], M.E. Kahoui has shown that if $R$ is a polynomial ring over $\mathbb{C}$, $A$ an $\mathbb{A}^3$-fibration over $R$, and $W$ a residual variable of $A$ then $A$ is stably polynomial over $R[W]$. In this article we show that the above result holds over any Noetherian domain $R$ provided the module of differentials $\Omega_R(A)$ of the affine fibration $A$ (which is necessarily a projective $A$-module by a theorem of Asanuma) is a stably free $A$-module.

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Prosenjit Das, Amartya K. Dutta. 2020-02-06. A Note on Residual Variables of an Affine Fibration. https://doi.org/10.1016/j.jpaa.2014.02.005

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