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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yekutieli, A., Zhang, J.J. Dualizing complexes and perverse sheaves on noncommutative ringed schemes. Sel. math., New ser. 12, 137–177 (2006). https://doi.org/10.1007/s00029-006-0022-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00029-006-0022-4