English

Homology of complexes over finite tensor categories

K-Theory and Homology 2023-01-19 v1 Category Theory Rings and Algebras Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2301.07578,
  title  = {Homology of complexes over finite tensor categories},
  author = {Petter Andreas Bergh},
  journal= {arXiv preprint arXiv:2301.07578},
  year   = {2023}
}

Comments

19 pages