Moduli schemes of generically simple Azumaya modules
代数几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0411094,
title = {Moduli schemes of generically simple Azumaya modules},
author = {Norbert Hoffmann and Ulrich Stuhler},
journal= {arXiv preprint arXiv:math/0411094},
year = {2007}
}
备注
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