Comptes Rendus
Algebra, Algebraic geometry
Noncommutative tensor triangulated categories and coherent frames
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1415-1427.

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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DOI: 10.5802/crmath.461
Classification: 06D22, 18F70, 18G80, 18M05, 54Exx, 55P43

Vivek Mohan Mallick 1; Samarpita Ray 2

1 Department of Mathematics, Indian Institute of Science Education and Research (IISER) Pune, Pune 411008, India
2 Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, South Korea
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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