Abstract local cohomology functors
Yuji Yoshino, Takeshi Yoshizawa
TL;DR
This paper introduces the concept of abstract local cohomology functors, characterizing derived functors of local cohomology as elements within this new framework, unifying various cohomology theories.
Contribution
It defines abstract local cohomology functors and characterizes derived local cohomology functors as specific instances within this new abstract framework.
Findings
Derived functors of local cohomology are characterized as elements of the set of all abstract local cohomology functors.
The framework unifies ordinary and generalized local cohomology functors.
Provides a new perspective on local cohomology theories.
Abstract
We propose to define the notion of abstract local cohomology functors. The derived functors of the ordinary local cohomology functor with support in the closed subset defined by an ideal and the generalized local cohomology functor associated with a given pair of ideals are characterized as elements of the set of all the abstract local cohomology functors.
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 · Homotopy and Cohomology in Algebraic Topology