## Moduli schemes of generically simple Azumaya modules

### Summary

Summary: 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.

14J60, 16H05

### Keywords/Phrases

moduli space, torsion free sheaf, Azumaya module, brandt groupoid