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.
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Vivek Mohan Mallick 1; Samarpita Ray 2
@article{CRMATH_2023__361_G9_1415_0, author = {Vivek Mohan Mallick and Samarpita Ray}, title = {Noncommutative tensor triangulated categories and coherent frames}, journal = {Comptes Rendus. Math\'ematique}, pages = {1415--1427}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.461}, language = {en}, }
TY - JOUR AU - Vivek Mohan Mallick AU - Samarpita Ray TI - Noncommutative tensor triangulated categories and coherent frames JO - Comptes Rendus. Mathématique PY - 2023 SP - 1415 EP - 1427 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.461 LA - en ID - CRMATH_2023__361_G9_1415_0 ER -
Vivek Mohan Mallick; Samarpita Ray. Noncommutative tensor triangulated categories and coherent frames. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1415-1427. doi : 10.5802/crmath.461. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.461/
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