Local structure of Schelter-Procesi smooth orders

Le Bruyn, Lieven

doi:10.1090/S0002-9947-00-02567-8

Local structure of Schelter-Procesi smooth orders
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by Lieven Le Bruyn

Trans. Amer. Math. Soc. 352 (2000), 4815-4841

DOI: https://doi.org/10.1090/S0002-9947-00-02567-8

Published electronically: June 14, 2000

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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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