2018-12-062018-12-062005Hoffmann, N., Stuhler, U. (2005) 'Moduli Schemes of Generically Simple Azumaya Modules.' Documenta Mathematica 10, pp. 369-389.http://hdl.handle.net/10395/2507Moduli 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.enghttps://www.math.uni-bielefeld.de/documenta/vol-10/12.pdfModuli spaceTorsion free sheafAzumaya moduleBrandt groupoidArticlearXiv:math/0411094v2