Geodesic
Algèbre, Gométrie algébrique
Noncommutative tensor triangulated categories and coherent frames
Mallick, Vivek Mohan1  ; Ray, Samarpita2
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
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1415-1427

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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

Mallick, Vivek Mohan 1 ; Ray, Samarpita 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Noncommutative tensor triangulated categories and coherent frames},
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Mallick, Vivek Mohan; Ray, Samarpita. Noncommutative tensor triangulated categories and coherent frames. Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1415-1427. doi: 10.5802/crmath.461

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