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 ⊂ 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

Primary: 20C05

Secondary: 14L15, 16S34, 16S35, 16W30

Authors