#### Vol. 2, No. 4, 2008

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On the algebra of some group schemes

### Daniel Ferrand

Vol. 2 (2008), No. 4, 435–466
##### Abstract

The algebra of a finite group over a field $k$ of characteristic zero is known to be a projective separable $k$-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 $k$-algebra is a quotient of the group algebra of a suitable group scheme, finite étale over $k$. In particular, any finite separable field extension $K\subset L$, even a noncyclotomic one, may be generated by a finite étale $K$-group scheme.

##### Keywords
group algebra, finite étale group scheme, Weil restriction, separable algebra
##### Mathematical Subject Classification 2000
Primary: 20C05
Secondary: 14L15, 16S34, 16S35, 16W30