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.