Separable equivalences, finitely generated cohomology and finite tensor categories
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.10775
 Bibcode:
 2021arXiv210910775B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  KTheory and Homology;
 Mathematics  Quantum Algebra;
 Mathematics  Rings and Algebras;
 16E40;
 16T05;
 18M05;
 19D23
 EPrint:
 24 pages