2021/09/22 by Petter Andreas Bergh, Bergh, Petter Andreas · 1 citation
Mathematics · #16E40 #16T05 #18M05 #19D23 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2109.10775
openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.