Étale group scheme

In mathematics, more precisely in algebra, an étale group scheme is a certain kind of group scheme.

Definition

A finite group scheme $G$ over a field $K$ is called an étale group scheme if it is represented by an étale K-algebra $\mathfrak{\Re }$, i.e. if $\mathfrak{\Re }{\otimes }_K\overline{K}$ is isomorphic to $\overline{K}\times ...\times \overline{K}$.

References

• John Voight, Introduction to group schemes, Dartmouth College (lecture notes), https://math.dartmouth.edu/~jvoight/notes/274-Schoof.pdf