A classical result of Bondal and Van den Bergh states that the derived category of quasi-coherent
sheaves on a quasi-compact, quasi-separated scheme is generated by a single compact generator.
This implies the dg affinity of these schemes. After reviewing some elements of the theory of
Deformation Quantization modules (DQ-modules), I will introduce a triangulated category that
should be thought of as the deformation of the derived category of quasi-coherent sheaves
while quantizing the structure sheaf of the variety. Then, I will prove the dg affinity of DQ-modules.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/158