Geodesic
Moduli schemes of generically simple Azumaya modules
Documenta mathematica, Tome 10 (2005), pp. 369-389
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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.
DOI : 10.4171/dm/194
Classification : 14J60, 16H05
Mots-clés : moduli space, torsion free sheaf, Azumaya module, brandt groupoid 
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     author = {Ulrich Stuhler and Norbert Hoffmann},
     title = {Moduli schemes of generically simple {Azumaya} modules},
     journal = {Documenta mathematica},
     pages = {369--389},
     year = {2005},
     volume = {10},
     doi = {10.4171/dm/194},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/194/}
}
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Ulrich Stuhler; Norbert Hoffmann. Moduli schemes of generically simple Azumaya modules. Documenta mathematica, Tome 10 (2005), pp. 369-389. doi: 10.4171/dm/194

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