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.