Alladi Ramakrishnan Hall

Dualizing Complexes in the Noncommutative Arithmetic Context

Rishi Vyas

Ben Gurion University

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.