Comptes Rendus
Homological algebra/Algebraic geometry
A topological nullstellensatz for tensor-triangulated categories
Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 365-375.

Let Spec(T) be the spectrum of a tensor-triangulated category (T,,1). We show that there is a homeomorphism between the spectral space of radical thick tensor ideals in (T,,1) and the collection of open subsets of Spec(T) in inverse topology. In fact, we prove a more general result in terms of supports on (T,,1) and work by combining methods from commutative algebra, topology and tensor triangular geometry.

Soit Spec(T) le spectre d'une catégorie triangulée tensorielle (T,,1) et notons par Spec(T)inv la topologie inverse sur Spec(T). Nous montrons qu'on dispose d'un homéomorphisme entre l'espace spectral des idéaux radicaux de (T,,1) et l'espace des sous-ensembles ouverts de Spec(T)inv. En fait, nous obtenons un résulat plus général en termes des données de support sur (T,,1) en utilisant des idées provenant d'algèbre commutative, de topologie et de géométrie triangulée tensorielle.

Published online:
DOI: 10.1016/j.crma.2018.02.012

Abhishek Banerjee 1

1 Department of Mathematics, Indian Institute of Science, Bangalore-560012, India
     author = {Abhishek Banerjee},
     title = {A topological nullstellensatz for tensor-triangulated categories},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {365--375},
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     number = {4},
     year = {2018},
     doi = {10.1016/j.crma.2018.02.012},
     language = {en},
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Abhishek Banerjee. A topological nullstellensatz for tensor-triangulated categories. Comptes Rendus. Mathématique, Volume 356 (2018) no. 4, pp. 365-375. doi : 10.1016/j.crma.2018.02.012.

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