Geodesic
Finite Group Schemes of Essential Dimension One
Documenta mathematica, Tome 25 (2020), pp. 55-64.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $\mathrm{PGL}_{2/k}$. We use this to give an explicit classification of all infinitesimal group schemes of essential dimension one over any field and a characterisation of all finite group schemes of essential dimension one over algebraically closed fields.
Classification : 14L15, 12G05
Keywords: essential dimension, finite group schemes 
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     title = {Finite {Group} {Schemes} of {Essential} {Dimension} {One}},
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Fakhruddin, Najmuddin. Finite Group Schemes of Essential Dimension One. Documenta mathematica, Tome 25 (2020), pp. 55-64. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a70/