Noncommutative tensor triangulated categories and coherent frames

Vivek Mohan Mallick; Samarpita Ray

doi:10.5802/crmath.461

Algèbre, Gométrie algébrique

Noncommutative tensor triangulated categories and coherent frames

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

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1415-1427.

Résumé

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.

Reçu le : 2022-07-05
Révisé le : 2022-12-17
Accepté le : 2022-12-29
Publié le : 2023-11-10

DOI : 10.5802/crmath.461

Classification : 06D22, 18F70, 18G80, 18M05, 54Exx, 55P43

Affiliations des auteurs :

Vivek Mohan Mallick ¹ ; Samarpita Ray ²

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},
     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},
}

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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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