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

References

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