Homology of complexes over finite tensor categories

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 project...

Full description

Saved in:
Bibliographic Details
Published in:Journal of noncommutative geometry 2024-03, Vol.19 (1), p.249-268
Main Author: Bergh, Petter Andreas
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1661-6952
1661-6960
DOI:10.4171/jncg/564