Strong global dimension of commutative rings and schemes
Ragnar-Olaf Buchweitz, Hubert Flenner
TL;DR
This paper characterizes noetherian commutative rings and schemes with finite strong global dimension, which measures the maximum length of certain indecomposable perfect complexes in their derived categories.
Contribution
It provides a complete characterization of noetherian rings and schemes with finite strong global dimension, extending previous understanding in derived category theory.
Findings
Characterization of noetherian rings with finite strong global dimension
Extension of the characterization to noetherian schemes
Insight into the structure of perfect complexes in derived categories
Abstract
The strong global dimension of a ring is the supremum of the length of perfect complexes that are indecomposable in the derived category. In this note we characterize the noetherian commutative rings that have finite strong global dimension. We also give a similar characterization for arbitrary noetherian schemes.
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 · Rings, Modules, and Algebras · Commutative Algebra and Its Applications