Finite Group Schemes of Essential Dimension One
Najmuddin Fakhruddin · Documenta Mathematica · 2020
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.