Are finiteness conditions derived invariant?
Algebra Seminar
12th November 2024, 4:00 pm – 5:00 pm
Fry Building, 2.04
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.
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