Separable equivalences, finitely generated cohomology and finite tensor categories

Author:

Bergh Petter Andreas

Abstract

AbstractWe 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.

Funder

NTNU Norwegian University of Science and Technology

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Reference51 articles.

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