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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Local structure of Schelter-Procesi smooth orders


Author: Lieven Le Bruyn
Journal: Trans. Amer. Math. Soc. 352 (2000), 4815-4841
MSC (2000): Primary 16R30
Published electronically: June 14, 2000
MathSciNet review: 1695028
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Abstract:

In this paper we give the étale local classification of Schelter-Procesi smooth orders in central simple algebras. In particular, we prove that if $\Delta$ is a central simple $K$-algebra of dimension $n^2$, where $K$is a field of trancendence degree $d$, then there are only finitely many étale local classes of smooth orders in $\Delta$. This result is a non-commutative generalization of the fact that a smooth variety is analytically a manifold, and so has only one type of étale local behaviour.


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Additional Information

Lieven Le Bruyn
Affiliation: Departement Wiskunde, University of Antwerp (UIA) B.2610, Antwerp, Belgium
Email: lebruyn@wins.uia.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02567-8
PII: S 0002-9947(00)02567-8
Received by editor(s): July 10, 1997
Published electronically: June 14, 2000
Additional Notes: The author is a research director of the NFWO
Article copyright: © Copyright 2000 American Mathematical Society