Openness with respect to levels in triangulated categories
Souvik Dey, Jian Liu, Liran Shaul
TL;DR
This paper investigates the openness of levels of compact objects in triangulated categories with ring actions, extending previous results and applying to various derived and singularity categories.
Contribution
It generalizes existing results on openness of levels in triangulated categories to broader contexts with ring actions.
Findings
Proves a general theorem on openness of levels in compact objects
Applies results to derived categories of rings and DG rings
Provides insights into the structure of singularity categories
Abstract
Given a compactly generated triangulated category equipped with an action of a graded-commutative Noetherian ring , generalizing results of Letz, we prove a general result concerning the openness with respect to levels of compact objects in . Applications are given to derived categories of commutative Noetherian rings, derived categories of commutative Noetherian DG rings and singularity categories.
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Taxonomy
TopicsAdvanced Algebra and Logic