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Openness with respect to levels in triangulated categories (2505.14353v1)
Published 20 May 2025 in math.AC, math.CT, and math.RA
Abstract: Given a compactly generated triangulated category $\mathcal{T}$ 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 $\mathcal{T}$. Applications are given to derived categories of commutative Noetherian rings, derived categories of commutative Noetherian DG rings and singularity categories.