# Dualizing complexes and perverse sheaves on noncommutative ringed schemes Academic Article

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### abstract

• A quasi-coherent ringed scheme is a pair (X, $$\mathcal{A}$$), where X is a scheme, and $$\mathcal{A}$$ is a noncomutative quasi-coherent $$\mathcal{O}_X$$ -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.

### publication date

• January 1, 2006