English

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.

Keywords

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