# Essential dimension of the spin groups in characteristic 2

## TL;DR

This paper calculates the essential dimension of spin groups over fields of characteristic 2, revealing that for large n it matches the dimension in other characteristics, which is unexpectedly larger than that of orthogonal groups.

## Contribution

It provides the first determination of the essential dimension of Spin(n) in characteristic 2 for n ≥ 15, showing it matches the characteristic not 2 case, and also covers smaller n cases.

## Key findings

- Essential dimension of Spin(n) in characteristic 2 is exponential in n for n ≥ 15.
- Essential dimension matches the characteristic not 2 case for large n.
- Essential dimension of Spin(n) in characteristic 2 is smaller than that of orthogonal groups.

## 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. This is surprising in that 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.