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arXiv · 2509.20853

On the representation type of a finite tensor category

Petter Andreas Bergh·Karin Erdmann·Julia Yael Plavnik·Sarah Witherspoon
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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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Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik, Sarah Witherspoon. 2025-09-25. On the representation type of a finite tensor category. https://arxiv.org/abs/2509.20853

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