2023/01/18 by Petter Andreas Bergh, Bergh, Petter Andreas
Mathematics · #16E40 #16T05 #18E10 #18G35 #18M05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2301.07578
openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize a recent result by J.F. Carlson to finite tensor categories having finitely generated cohomology. Specifically, we show that if the Krull dimension of the cohomology ring is sufficiently large, then there exist infinitely many non-isomorphic and nontrivial bounded complexes of projective objects, and with small homology. We also prove a version for finite dimensional algebras with finitely generated cohomology.