48 citations · 140 across the 46 of their papers we have counts for
6 papers · 1 filter
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 without the tensor product property
Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon
We show that over a perfect field, every non-semisimple finite tensor category with finitely generated cohomology embeds into a larger such category where the tensor product proper…
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…
Support varieties for finite tensor categories: Complexity, realization, and connectedness
Petter Andreas Bergh, Julia Yael Plavnik, Sarah Witherspoon
We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projecti…
The representation dimension of quantum complete intersections
Petter Andreas Bergh, Steffen Oppermann
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most tw…