Geodesic
Finite Group Schemes of Essential Dimension One
Documenta mathematica, Tome 25 (2020), pp. 55-64
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We prove that if a finite group scheme G over a field k has essential dimension one, then it embeds in PGL2/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.
DOI : 10.4171/dm/737
Classification : 12G05, 14L15
Mots-clés : essential dimension, finite group schemes 
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     author = {Najmuddin Fakhruddin},
     title = {Finite {Group} {Schemes} of {Essential} {Dimension} {One}},
     journal = {Documenta mathematica},
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     doi = {10.4171/dm/737},
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Najmuddin Fakhruddin. Finite Group Schemes of Essential Dimension One. Documenta mathematica, Tome 25 (2020), pp. 55-64. doi: 10.4171/dm/737

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