#### 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.

Done