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ON SEPARABLE $\mathbb{A}^{2}$ AND $\mathbb{A}^{3}$-FORMS
Published online by Cambridge University Press: 26 December 2018
Abstract
In this paper, we will prove that any $\mathbb{A}^{3}$-form over a field $k$ of characteristic zero is trivial provided it has a locally nilpotent derivation satisfying certain properties. We will also show that the result of Kambayashi on the triviality of separable $\mathbb{A}^{2}$-forms over a field $k$ extends to $\mathbb{A}^{2}$-forms over any one-dimensional Noetherian domain containing $\mathbb{Q}$.
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- © 2018 Foundation Nagoya Mathematical Journal
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