Abstract
An action of a finite group A / p P for a prime p on the affine plane A 2 in characteristic zero can be deformed to an action of the local group scheme μ p on A 2 in positive characteristic. Given an action of μ p on A 2, one may ask conversely when this action is a deformation of an action of Z / p Z . We shall show that the linearizability condition of the action of μ p is a good candidate for a necessary and sufficient condition.
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