  A quasi-coherent ringed scheme is a pair (X,A), where X is a scheme, and A is
a noncommutative quasi-coherent O_X-ring. We introduce dualizing complexes over
quasi-coherent ringed schemes and study their properties. For a separated
differential quasi-coherent ringed scheme of finite type over a field, we prove
existence and uniqueness of a rigid dualizing complex. In the proof we use the
theory of perverse coherent sheaves in order to glue local pieces of the rigid
dualizing complex into a global complex.
