Moduli schemes of generically simple Azumaya modules

Details Moduli schemes of generically simple Azumaya modules Moduli schemes of generically simple Azumaya modules

2004-11-04

arxiv.org/abs/math/0411094v2

Documenta Math. 10 (2005) 369--389

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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