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 ${\displaystyle G}$ over a field ${\displaystyle K}$ is called an étale group scheme if it is represented by an étale K-algebra ${\displaystyle {\mathfrak {R}}}$, i.e. if ${\displaystyle {\mathfrak {R}}\otimes _{K}{\bar {K}}}$ is isomorphic to ${\displaystyle {\bar {K}}\times ...\times {\bar {K}}}$.

References

• John Voight, Introduction to group schemes (PDF), Dartmouth College (lecture notes)