Relative singularity categories, Gorenstein objects and silting theory

Jiaqun Wei

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arXiv · 1504.06738

Relative singularity categories, Gorenstein objects and silting theory

Jiaqun Wei

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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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BibTeX RIS

Jiaqun Wei. 2015-04-25. Relative singularity categories, Gorenstein objects and silting theory. https://arxiv.org/abs/1504.06738

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