Support varieties for finite tensor categories: Complexity and tensor products

Authors:
  • JPJulia Yael Plavnik
    Julia Yael Plavnik
  • SWSarah Witherspoon
    Sarah Witherspoon
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Abstract
We advance support variety theory for finite tensor categories. We prove that the dimension of the support variety of an object is equal to the rate of growth of a minimal projective resolution as measured by Frobenius-Perron dimension. We ask when the tensor product property holds, that is, when is the support variety of a tensor product of objects equal to the intersection of their support varieties? We discuss some known and some new settings in which objects do or do not possess this property as well as a weaker property involving projectivity.