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.
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