Jon Carlson - Locally dualizable modules abound

This is joint work with Srikanth Iyengar. The derived category of a
commutative local noetherian ring and the module category of a modular group algebra are tensor triangulated categories. A dualizable
object in such a category is one that has a dual that is compatible
with the tensor structure. The question that we address in this paper
is whether the subcategory dualizable objects in certain colocal sub-
categories is the idempotent closure of image of the compact objects
under the local cohomology functor associated to the subcategory. In
this lecture, I will try to explain what all of these words mean, why one
might care about such a question and how we get a negative answer is
certain cases.