Algebra & Number Theory
- Algebra Number Theory
- Volume 2, Number 4 (2008), 435-466.
On the algebra of some group schemes
The algebra of a finite group over a field of characteristic zero is known to be a projective separable -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 -algebra is a quotient of the group algebra of a suitable group scheme, finite étale over . In particular, any finite separable field extension , even a noncyclotomic one, may be generated by a finite étale -group scheme.
Algebra Number Theory, Volume 2, Number 4 (2008), 435-466.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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