The finitistic dimension of a triangulated category
arXiv:2307.12671
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.
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