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ON SEPARABLE $\mathbb{A}^{2}$ AND $\mathbb{A}^{3}$ -FORMS


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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Nagoya Mathematical Journal
  • ISSN: 0027-7630
  • EISSN: 2152-6842
  • URL: /core/journals/nagoya-mathematical-journal
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