Essential dimension of the spin groups in characteristic 2

Abstract

We determine the essential dimension of the spin group Spin$(n)$ as an algebraic group over a field of characteristic 2, for $n$ at least 15. In this range, the essential dimension is the same as in characteristic not 2. In particular, it is exponential in n. In contrast, the essential dimension of the orthogonal groups is smaller in characteristic 2. We also find the essential dimension of Spin$(n)$ in characteristic 2 for $n$ at most 10.