Local dualisable objects in local algebra
Dave Benson, Srikanth B. Iyengar, Henning Krause, and Julia Pevtsova
TL;DR
This paper investigates dualisable objects within specific subcategories of tensor triangulated categories, especially focusing on the derived category of a commutative noetherian ring, and provides a cohomological criterion for their detection.
Contribution
It introduces a cohomological criterion for identifying local dualisable objects in the derived category of a commutative noetherian ring, extending the understanding of dualisability in tensor triangulated categories.
Findings
Established a cohomological criterion for local dualisable objects.
Analyzed dualisability in minimal subcategories of tensor triangulated categories.
Discussed generalizations to related mathematical contexts.
Abstract
We discuss dualisable objects in minimal subcategories of compactly generated tensor triangulated categories, paying special attention to the derived category of a commutative noetherian ring. A cohomological criterion for detecting these local dualisable objects is established. Generalisations to other related contexts are discussed.
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 · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology