Support varieties are important tools in representation theory, for example representations of finite groups and finite group schemes. Much of the theory holds for finite tensor categories generally and in related settings, while much is still unknown. In this talk we will focus on a tensor product property for support varieties, and a reduction to the indecomposable periodic objects. As a consequence of the reduction, the tensor product property holds for all symmetric finite tensor categories over algebraically closed fields of characteristic 0. This is joint work with Petter Andreas Bergh and Julia Yael Plavnik.
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