Étale group scheme
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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
Original source: https://en.wikipedia.org/wiki/Étale group scheme.
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