In mathematics, more precisely in algebra, an étale group scheme is a certain kind of group scheme.
A finite group scheme G {\displaystyle G} over a field K {\displaystyle K} is called an étale group scheme if it is represented by an étale K-algebra R {\displaystyle {\mathfrak {R}}} , i.e. if R ⊗ K K ¯ {\displaystyle {\mathfrak {R}}\otimes _{K}{\bar {K}}} is isomorphic to K ¯ × . . . × K ¯ {\displaystyle {\bar {K}}\times ...\times {\bar {K}}} .
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