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On the cohomology of finite tensor categories
Petter Andreas Bergh
It has been conjectured that finite tensor categories have finitely generated cohomology. We show that this is equivalent to finitely generated Hochschild cohomology for the endomo…
On the representation type of a finite tensor category
Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik +1
Given an exact module category over a finite tensor category with finitely generated cohomology, we show that if there exists an object of complexity at least three, then the categ…
Support varieties for finite tensor categories: the tensor product property
Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon
We show that in a finite tensor category, the tensor product property holds for support varieties if and only if it holds between indecomposable periodic objects. We apply this to…