Non-commutative virtual structure sheaves

The moduli spaces of stable sheaves on algebraic varieties admit certain non-commutative structures, which I call quasi NC structures. In this talk, I show that the quasi NC structures on these moduli spaces arise as truncations of smooth quasi NC dg-schemes. This result is used to introduce the notion of NC virtual structure sheaves on the moduli spaces of stable sheaves which admit perfect obstruction theories. I will then show that the NC virtual structure sheaves are described in terms of Schur complexes of perfect obstruction theories.