Moduli Schemes of Generically Simple Azumaya Modules

Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion free A-module sheaves have a projective coarse moduli scheme; it is smooth and even symplectic if X is an abelian or K3 surface and A is Azumaya. We explain a relation to the classical theory of the Brandt groupoid.

2000 Mathematics Subject Classification: 14J60 (Primary), 16H05

Keywords and Phrases: Moduli space, torsion free sheaf, Azumaya module, Brandt groupoid

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