Blt Azumaya algebras and moduli of maximal orders

Details Blt Azumaya algebras and moduli of maximal orders Blt Azumaya algebras and moduli of maximal orders

2011-03-18

arxiv.org/abs/1103.3713v1

Mathematics

Algebraic Geometry

19 pages, preliminary version, comments welcome!

Scientific paper

We study moduli spaces of maximal orders in a ramified division algebra over the function field of a smooth projective surface. As in the case of moduli of stable commutative surfaces, we show that there is a Koll\'ar-type condition giving a better moduli problem with the same geometric points: the stack of blt Azumaya algebras. One virtue of this refined moduli problem is that it admits a compactification with a virtual fundamental class.

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