Dualizing complexes were first introduced in commutative algebra and algebraic geometry by Grothendieck and play a fundamental role in Serre-Grothendieck duality theory for schemes. The notion of a dualizing complex was extended to noncommutative ring theory by Yekutieli. There are existence theorems for dualizing complexes in the noncommutative context, due to Van den Bergh, Wu, Zhang, and Yekutieli amongst others.

Most considerations of dualizing complexes over noncommutative rings are for algebras defined over fields. There are technical difficulties involved in extending this theory to algebras defined over more general commutative base rings. In this talk, we will describe these challenges and how to get around them. Time permitting, we will end by presenting an existence theorem for dualizing complexes in this more general setting.

The material described in this talk is work in progress, carried out jointly with Amnon Yekutieli.

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