Balmer initiated the study of separable commutative algebras (tt-rings in short) in tt-geometry: these are commutative algebras for which the multiplication map admits a bimodule section. Their importance has grown in recent years due to the fact that the category of modules over a tt-ring is again a tt-category, and that tt-rings allow to prove strong descent results. However, the classification of all tt-rings in a tt-category is an open problem in many cases of interest. In this talk, I will relate the notion of tt-ring to the notion of finite cover due to Mathew, and use this connection to provide classification results for tt-rings in some special cases of interest.
This is joint work with Niko Naumann.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
