The finitistic dimension of a triangulated category
Henning Krause
TL;DR
This paper introduces the finitistic dimension for triangulated categories and establishes its finiteness condition in relation to the small finitistic dimension of rings, linking categorical and ring-theoretic properties.
Contribution
It defines the finitistic dimension for triangulated categories and proves its finiteness criterion aligns with the small finitistic dimension of rings.
Findings
Finitistic dimension is finite iff the small finitistic dimension of the ring is finite.
Establishes a connection between categorical and algebraic properties.
Provides a new perspective on the structure of perfect complexes.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra