Finite tensor categories are important generalizations of the categories of finite-dimensional modules of finite-dimensional Hopf algebras. There are two support theories for them, the cohomological one and one based on the noncommutative Balmer spectrum of the corresponding stable module category. We will describe general results linking the two types of support via a new notion of categorical center of the cohomology ring of a finite tensor category and will state a conjecture giving the exact relation. The construction and results will be illustrated with various examples.
This is joint with Daniel Nakano (Univ Georgia) and Kent Vashaw (MIT).
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
