Abstract
The algebra of a finite group over a field of characteristic zero is known to be a projective separable -algebra; but these separable algebras are of a very special type, characterized by Brauer and Witt.
In contrast with that, we prove that any projective separable -algebra is a quotient of the group algebra of a suitable group scheme, finite étale over . In particular, any finite separable field extension , even a noncyclotomic one, may be generated by a finite étale -group scheme.
Citation
Daniel Ferrand. "On the algebra of some group schemes." Algebra Number Theory 2 (4) 435 - 466, 2008. https://doi.org/10.2140/ant.2008.2.435
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