Relative singularity categories and singular equivalences
| العنوان: | Relative singularity categories and singular equivalences |
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| المؤلفون: | Rasool Hafezi |
| المصدر: | Journal of Homotopy and Related Structures. 16:487-516 |
| بيانات النشر: | Springer Science and Business Media LLC, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Noetherian, Subcategory, Path (topology), Noetherian ring, Algebra and Number Theory, Mathematics::Commutative Algebra, Homotopy category, Triangular matrix, Lift (mathematics), Combinatorics, Singularity, Mathematics::Category Theory, Geometry and Topology, Mathematics |
| الوصف: | Let R be a right noetherian ring. We introduce the concept of relative singularity category $$\Delta _{\mathcal {X} }(R)$$ of R with respect to a contravariantly finite subcategory $$\mathcal {X} $$ of $${\text {{mod{-}}}}R.$$ Along with some finiteness conditions on $$\mathcal {X} $$ , we prove that $$\Delta _{\mathcal {X} }(R)$$ is triangle equivalent to a subcategory of the homotopy category $$\mathbb {K} _\mathrm{{ac}}(\mathcal {X} )$$ of exact complexes over $$\mathcal {X} $$ . As an application, a new description of the classical singularity category $$\mathbb {D} _\mathrm{{sg}}(R)$$ is given. The relative singularity categories are applied to lift a stable equivalence between two suitable subcategories of the module categories of two given right noetherian rings to get a singular equivalence between the rings. In different types of rings, including path rings, triangular matrix rings, trivial extension rings and tensor rings, we provide some consequences for their singularity categories. |
| تدمد: | 1512-2891 2193-8407 |
| DOI: | 10.1007/s40062-021-00289-1 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_________::5fde193a0f62879cb25bba7280e9d5a8 https://doi.org/10.1007/s40062-021-00289-1 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi...........5fde193a0f62879cb25bba7280e9d5a8 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15122891 21938407 |
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| DOI: | 10.1007/s40062-021-00289-1 |