On seperable \(\mathbb{A}^2\) and \(\mathbb{A}^3\)-forms. (English) Zbl 1454.14148
Summary: We 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 \(\mathbb{Q}\).
MSC:
| 14R10 | Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) |
| 13B25 | Polynomials over commutative rings |
| 12F10 | Separable extensions, Galois theory |
| 14R25 | Affine fibrations |
| 13A50 | Actions of groups on commutative rings; invariant theory |
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