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2009 Lifting of the additive group scheme actions
Kayo Masuda, Masayoshi Miyanishi
Tohoku Math. J. (2) 61(2): 267-286 (2009). DOI: 10.2748/tmj/1245849448


Let $B$ be a normal affine $\boldsymbol{C}$-domain and let $A$ be a $\boldsymbol{C}$-subalgebra of $B$ such that $B$ is a finite $A$-module. Let $\delta$ be a locally nilpotent derivation on $A$. Then $\delta$ lifts uniquely to the quotient field $L$ of $B$, which we denote by $\Delta$. We consider when $\Delta$ is a locally nilpotent derivation of $B$. This is a classical subject treated in [17, 19, 16]. We are interested in the case where $A$ is the $G$-invariant subring of $B$ when a finite group $G$ acts on $B$. As a related topic, we treat in the last section the finite coverings of log affine pseudo-planes in terms of the liftings of the $\boldsymbol{A}^1$-fibrations associated with locally nilpotent derivations.


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Kayo Masuda. Masayoshi Miyanishi. "Lifting of the additive group scheme actions." Tohoku Math. J. (2) 61 (2) 267 - 286, 2009.


Published: 2009
First available in Project Euclid: 24 June 2009

zbMATH: 1190.14065
MathSciNet: MR2541410
Digital Object Identifier: 10.2748/tmj/1245849448

Primary: 14R20
Secondary: 14R25

Rights: Copyright © 2009 Tohoku University


Vol.61 • No. 2 • 2009
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