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

Published online by Cambridge University Press:  26 December 2018

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

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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Article
Copyright
© 2018 Foundation Nagoya Mathematical Journal

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