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Finite group schemes of essential dimension one
Published 7 Aug 2019 in math.AG | (1908.02438v2)
Abstract: We prove that if a finite group scheme $G$ over a field $k$ has essential dimension one, then it embeds in $PGL_{2/k}$. 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.
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