The finitistic dimension of a triangulated category
Category Theory
2024-09-04 v3 Algebraic Geometry
Representation Theory
Abstract
The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
Cite
@article{arxiv.2307.12671,
title = {The finitistic dimension of a triangulated category},
author = {Henning Krause},
journal= {arXiv preprint arXiv:2307.12671},
year = {2024}
}
Comments
8 pages. Added an appendix about the big finitistic dimension. Final version that has been accepted for publication with the Proceedings of the American Mathematical Society