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

Part of: Ring extensions and related topics Affine geometry Field extensions General commutative ring theory

Published online by Cambridge University Press:  26 December 2018

AMARTYA KUMAR DUTTA ,
NEENA GUPTA  and
ANIMESH LAHIRI
AMARTYA KUMAR DUTTA
Affiliation:
Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India email amartya.28@gmail.com
NEENA GUPTA
Affiliation:
Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India email neenag@isical.ac.in
ANIMESH LAHIRI
Affiliation:
Swami Vivekananda Research Centre, Ramakrishna Mission Vidyamandira, P.O. Belur Math, Howrah 711202, India email 255alahiri@gmail.com
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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 $\mathbb{Q}$.

MSC classification

Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Secondary: 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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Type
Article
Information
Nagoya Mathematical Journal , Volume 239 , September 2020 , pp. 346 - 354
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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