Noncommutative tensor triangulated categories and coherent frames
We develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions. In particular, we provide a conceptual way of classifying radical thick tensor ideals of a noncommutative tensor triangulated catego...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.461/ |
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| _version_ | 1825206250786258944 |
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| author | Mallick, Vivek Mohan Ray, Samarpita |
| author_facet | Mallick, Vivek Mohan Ray, Samarpita |
| author_sort | Mallick, Vivek Mohan |
| collection | DOAJ |
| description | We develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions. In particular, we provide a conceptual way of classifying radical thick tensor ideals of a noncommutative tensor triangulated category using frame theoretic methods, recovering the universal support data in the process. We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology. |
| format | Article |
| id | doaj-art-988dff8a8ee54624a98c54c51115e18f |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-988dff8a8ee54624a98c54c51115e18f2025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91415142710.5802/crmath.46110.5802/crmath.461Noncommutative tensor triangulated categories and coherent framesMallick, Vivek Mohan0Ray, Samarpita1Department of Mathematics, Indian Institute of Science Education and Research (IISER) Pune, Pune 411008, IndiaCenter for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, South KoreaWe develop a point-free approach for constructing the Nakano–Vashaw–Yakimov–Balmer spectrum of a noncommutative tensor triangulated category under certain assumptions. In particular, we provide a conceptual way of classifying radical thick tensor ideals of a noncommutative tensor triangulated category using frame theoretic methods, recovering the universal support data in the process. We further show that there is a homeomorphism between the spectral space of radical thick tensor ideals of a noncommutative tensor triangulated category and the collection of open subsets of its spectrum in the Hochster dual topology.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.461/ |
| spellingShingle | Mallick, Vivek Mohan Ray, Samarpita Noncommutative tensor triangulated categories and coherent frames Comptes Rendus. Mathématique |
| title | Noncommutative tensor triangulated categories and coherent frames |
| title_full | Noncommutative tensor triangulated categories and coherent frames |
| title_fullStr | Noncommutative tensor triangulated categories and coherent frames |
| title_full_unstemmed | Noncommutative tensor triangulated categories and coherent frames |
| title_short | Noncommutative tensor triangulated categories and coherent frames |
| title_sort | noncommutative tensor triangulated categories and coherent frames |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.461/ |
| work_keys_str_mv | AT mallickvivekmohan noncommutativetensortriangulatedcategoriesandcoherentframes AT raysamarpita noncommutativetensortriangulatedcategoriesandcoherentframes |