Algebra & Number Theory

On the algebra of some group schemes

Daniel Ferrand

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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.

Article information

Source
Algebra Number Theory, Volume 2, Number 4 (2008), 435-466.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797269

Digital Object Identifier
doi:10.2140/ant.2008.2.435

Mathematical Reviews number (MathSciNet)
MR2411407

Zentralblatt MATH identifier
1167.20003

Subjects
Primary: 20C05: Group rings of finite groups and their modules [See also 16S34]
Secondary: 14L15: Group schemes 16S34: Group rings [See also 20C05, 20C07], Laurent polynomial rings 16S35: Twisted and skew group rings, crossed products 16W30

Keywords
group algebra finite étale group scheme Weil restriction separable algebra

Citation

Ferrand, Daniel. On the algebra of some group schemes. Algebra Number Theory 2 (2008), no. 4, 435--466. doi:10.2140/ant.2008.2.435. https://projecteuclid.org/euclid.ant/1513797269


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