Jeremy Rickard (University of Bristol) – Are finiteness conditions derived invariant?

This talk will not assume any knowledge of derived categories.

Two rings are "Morita equivalent" if they have equivalent module categories, and
if a property of rings depends only on the module category, then it is called
"Morita invariant". More generally, two rings are "derived equivalent" if they
have equivalent derived categories, and if a property of rings depends only on
the derived category, then it is called "derived invariant".

Fairly recently, Manuel Saorin asked me if I knew whether right coherence was a
derived invariant property. I didn't, but when my long term memory kicked in, I
realised that an example hidden in my 36 year old PhD thesis could be used to
give a counterexample.

Most of the talk will be an introduction to the background to this question and
variants, but it will finish with some fun examples of rings with strange
properties.