Relative singularity categories, Gorenstein objects and silting theory

J Wei - Journal of Pure and Applied Algebra, 2018 - Elsevier
We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

Relative singularity categories and Gorenstein‐projective modules

XW Chen - Mathematische Nachrichten, 2011 - Wiley Online Library
We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

Gorenstein silting complexes

W Cao, J WEI - Glasgow Mathematical Journal, 2022 - cambridge.org
We introduce and study the notion of Gorenstein silting complexes, which is a generalization
of Gorenstein tilting modules in Gorenstein-derived categories. We give the equivalent …

Silting reduction in extriangulated categories

Y Liu, P Zhou, Y Zhou, B Zhu - arXiv preprint arXiv:2108.07964, 2021 - arxiv.org
Presilting and silting subcategories in extriangulated categories were introduced by Adachi
and Tsukamoto recently. In this paper, we prove that the Gabriel-Zisman localization …

Gorenstein dimension of abelian categories arising from cluster tilting subcategories

Y Liu, P Zhou - Czechoslovak Mathematical Journal, 2021 - Springer
Abstract Let \ mathscr {C\} C be a triangulated category and \ mathscr {X\} X be a cluster
tilting subcategory of \ mathscr {C\} C. Koenig and Zhu showed that the quotient category …

[HTML][HTML] Change of rings and singularity categories

S Oppermann, C Psaroudakis, T Stai - Advances in Mathematics, 2019 - Elsevier
We investigate the behavior of singularity categories and stable categories of Gorenstein
projective modules along a morphism of rings. The natural context to approach the problem …

Relative singularity categories and Gorenstein-projective modules

XW Chen - arXiv preprint arXiv:0709.1762, 2007 - arxiv.org
We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

Stability of Gorenstein objects in triangulated categories

Z Wang, C Liang - arXiv preprint arXiv:1409.7274, 2014 - arxiv.org
Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

Singularity categories and singular equivalences for resolving subcategories

H Matsui, R Takahashi - Mathematische Zeitschrift, 2017 - Springer
Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

[HTML][HTML] Proper classes and Gorensteinness in extriangulated categories

J Hu, D Zhang, P Zhou - Journal of algebra, 2020 - Elsevier
Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous
generalization of exact categories and triangulated categories. A notion of proper class in an …