Openness with respect to levels in triangulated categories

2025/05/20 by Souvik Dey, Jian Liu, Dey, Souvik +3
Computer Science · #16E45 #18E35 #Advanced Algebra and Logic #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 18G80 #Rings and Algebras (math.RA) #Secondary 13D09

paper · pdf · doi:10.48550/arxiv.2505.14353

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compactly generated triangulated category T equipped with an action of a graded-commutative Noetherian ring R, generalizing results of Letz, we prove a general result concerning the openness with respect to levels of compact objects in T. Applications are given to derived categories of commutative Noetherian rings, derived categories of commutative Noetherian DG rings and singularity categories.

Citations

• Finitistic dimensions over commutative DG-rings
• Openness of various loci over Noetherian rings
• Openness of the regular locus and generators for module categories
• Homology over trivial extensions of commutative DG algebras
• Annihilation of cohomology and strong generation of module categories
• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Reflexivity and rigidity for complexes. I. Commutative rings
• Local cohomology and support for triangulated categories
• The stable derived category of a noetherian scheme
• Generators and representability of functors in commutative and noncommutative geometry

Related

• Torsion and complete dualizable objects in tensor-triangulated categories over a Noetherian ring
• Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories
• Lifting (co)stratifications between tensor triangulated categories
• Complete intersections and derived categories
• Dimensions of triangulated categories with respect to subcategories