Moduli schemes of generically simple Azumaya modules

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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.
20 pages. v2: generic setup slightly generalized (from rank one modules over a central division algebra to simple modules over a central simple algebra), a few references added

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Algebraic Geometry, 14J60 (Primary) 16H05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/95970

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411094
 http://arxiv.org/abs/math/0411094
 Documenta Math. 10 (2005) 369--389

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arXiv