Local structure of Schelter-Procesi smooth orders

In this paper we give the etale local classification of Schelter-Procesi sm ooth orders in central simple algebras. In particular, we prove that if Del ta is a central simple K-algebra of dimension n(2), where K is a field of t rancendence degree d, then there are only finitely many etale 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 o nly one type of etale local behaviour.