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

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.

group algebra, finite étale group scheme, Weil restriction, separable algebra
Mathematical Subject Classification 2000
Primary: 20C05
Secondary: 14L15, 16S34, 16S35, 16W30
Received: 12 December 2007
Revised: 31 March 2008
Accepted: 6 May 2008
Published: 15 June 2008
Daniel Ferrand
Université de Rennes 1
Campus de Beaulieu
35042 Rennes