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2008 On the algebra of some group schemes
Daniel Ferrand
Algebra Number Theory 2(4): 435-466 (2008). 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 KL, even a noncyclotomic one, may be generated by a finite étale K-group scheme.

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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

Information

Received: 12 December 2007; Revised: 31 March 2008; Accepted: 6 May 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1167.20003
MathSciNet: MR2411407
Digital Object Identifier: 10.2140/ant.2008.2.435

Subjects:
Primary: 20C05
Secondary: 14L15 , 16S34 , 16S35 , 16W30

Keywords: finite étale group scheme , group algebra , separable algebra , Weil restriction

Rights: Copyright © 2008 Mathematical Sciences Publishers

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