no. G9
Algèbre, Gométrie algébrique
Noncommutative tensor triangulated categories and coherent frames
Mallick, Vivek Mohan1  ; Ray, Samarpita2
1Department of Mathematics, Indian Institute of Science Education and Research (IISER) Pune, Pune 411008, India
2Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, South Korea
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, 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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Révisé le :
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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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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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