A Note on Residual Variables of an Affine Fibration
| Autor: | Das, Prosenjit, Dutta, Amartya K. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Pure and Applied Algebra, Volume 218, Issue 10 (2014), 1792-1799 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jpaa.2014.02.005 |
| Popis: | 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. Comment: 6 pages |
| Databáze: | arXiv |
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