Essential dimension of finite groups in prime characteristic

Abstract

Given a finite smooth group scheme $G$ over a field of characteristic $p>0$, we show that the essential dimension of $G$ at $p$ is $0$ when $p$ does not divide the order of $G$, and $1$ when it does.

7 pages. Added a new proof of a key lemma due to a referee, and made some more minor changes. Accepted for publication in Comptes Rendus Mathematique