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Relative singularity categories, Gorenstein objects and silting theory (1504.06738v1)

Published 25 Apr 2015 in math.RT, math.AC, math.AG, math.CT, and math.RA

Abstract: We study singularity categories through Gorenstein objects in triangulated categories and silting theory. Let ${\omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\mathcal{T}$. We introduce the notion of $\omega$-Gorenstein objects, which is far extended version of Gorenstein projective modules and Gorenstein injective modules in triangulated categories. We prove that the stable category $\underline{\mathcal{G}{\omega}}$, where $\mathcal{G}{\omega}$ is the subcategory of all ${\omega}$-Gorenstein objects, is a triangulated category and it is, under some conditions, triangle equivalent to the relative singularity category of $\mathcal{T}$ with respect to $\omega$.

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