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Blt Azumaya algebras and moduli of maximal orders

By Rajesh S. Kulkarni and Max Lieblich


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.Comment: 14 pages, comments still welcome

Topics: Mathematics - Algebraic Geometry, Mathematics - Rings and Algebras, 14D20, 16H10
Year: 2016
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