On the algebra of some group schemes

Ferrand, Daniel

doi:10.2140/ant.2008.2.435

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On the algebra of some group schemes

Daniel Ferrand

Vol. 2 (2008), No. 4, 435–466

DOI: 10.2140/ant.2008.2.435

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

Milestones

Received: 12 December 2007

Revised: 31 March 2008

Accepted: 6 May 2008

Published: 15 June 2008

Authors

Daniel Ferrand
IRMAR Université de Rennes 1 Campus de Beaulieu 35042 Rennes France

Vol. 2, No. 4, 2008