On the representation type of a finite tensor category

Published 25 Sep 2025 in math.QA, math.KT, and math.RT | (2509.20853v1)

Abstract: 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 category is of wild representation type. In particular, if the Krull dimension of the cohomology ring of the finite tensor category is at least three, then this category is wild.

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On the representation type of a finite tensor category (2 likes, 0 questions)