Comptes Rendus
no. 4
Homological algebra/Algebraic geometry
A topological nullstellensatz for tensor-triangulated categories
Claire Voisin
Abhishek Banerjee1
1Department of Mathematics, Indian Institute of Science, Bangalore-560012, India
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.

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

Abhishek Banerjee  1

1 Department of Mathematics, Indian Institute of Science, Bangalore-560012, India 
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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