Separable equivalences, finitely generated cohomology and finite tensor categories
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3112338Utgivelsesdato
2023Metadata
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- Institutt for matematiske fag [2528]
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Sammendrag
We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as conjectured by Etingof and Ostrik. Moreover, for such categories we also determine the representation dimension and the Rouquier dimension of the stable category. Finally, we recover a number of results on the cohomology of stably equivalent and singularly equivalent algebras.