Blt Azumaya algebras and moduli of maximal orders
  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. 
Rajesh S. Kulkarni and Max Lieblich
math.AG math.RA