Modules with reducible complexity
Petter Andreas Bergh
TL;DR
This paper introduces and investigates modules with reducible complexity over commutative Noetherian local rings, expanding understanding of their properties and implications for homology and cohomology vanishing.
Contribution
It defines the class of modules with reducible complexity, encompassing modules with finite complete intersection dimension, and explores their properties and homological behavior.
Findings
Modules with reducible complexity include all modules of finite complete intersection dimension.
Properties of these modules are characterized and analyzed.
Results are provided on the vanishing of homology and cohomology for these modules.
Abstract
For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given, together with results on the vanishing of homology and cohomology.
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
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras