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 ${\mathfrak {R}}$ , i.e. if ${\mathfrak {R}}\otimes _{K}{\bar {K}}$ is isomorphic to ${\bar {K}}\times ...\times {\bar {K}}$ .

gollark: Which is implemented in Rust.

gollark: osmarkscalculator™.

gollark: I just wrote these definitions, which are very definitive:``` ("Fac[0]", "1"), ("Fac[n]", "Fac[n-1]*n"), ("Fib[0]", "0"), ("Fib[1]", "1"), ("Fib[n]", "Fib[n-1] + Fib[n-2]")```

gollark: The product rule is written `("D[dx, a*b]", "D[dx, a] * b + D[dx, b] * a")` in osmarkscalculator™.

gollark: Yes.

References

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

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