论文标题
关于仿射纤维的残留变量的注释
A Note on Residual Variables of an Affine Fibration
论文作者
论文摘要
在最近的一篇论文[El 13]中，M.E. Kahoui表明，如果$ r $是$ \ Mathbb {c} $的多项式戒指，$ a $ a $ a $ a $ \ a $ \ mathbb {a}^3 $ - $ r $ $ r $，$ w $ w $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a in $ aby polynomial yes $ $ r [w]在本文中，我们表明上述结果在任何Noetherian域$ r $上都保留，前提是差差的模块$ω_r（a）$的仿射纤维化$ A $（这必然是Asanuma of Asanuma of Asanuma定理的投射$ a $ module）是稳定的免费$ a $ a $ a $ -module。
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 $Ω_R(A)$ of the affine fibration $A$ (which is necessarily a projective $A$-module by a theorem of Asanuma) is a stably free $A$-module.
