[Un théorème des zéros topologique pour les catégories triangulées tensorielles]
Soit le spectre d'une catégorie triangulée tensorielle et notons par la topologie inverse sur . Nous montrons qu'on dispose d'un homéomorphisme entre l'espace spectral des idéaux radicaux de et l'espace des sous-ensembles ouverts de . En fait, nous obtenons un résulat plus général en termes des données de support sur en utilisant des idées provenant d'algèbre commutative, de topologie et de géométrie triangulée tensorielle.
Let be the spectrum of a tensor-triangulated category . We show that there is a homeomorphism between the spectral space of radical thick tensor ideals in and the collection of open subsets of in inverse topology. In fact, we prove a more general result in terms of supports on and work by combining methods from commutative algebra, topology and tensor triangular geometry.
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@article{CRMATH_2018__356_4_365_0,
author = {Banerjee, Abhishek},
title = {A topological nullstellensatz for tensor-triangulated categories},
journal = {Comptes Rendus. Math\'ematique},
pages = {365--375},
publisher = {Elsevier},
volume = {356},
number = {4},
year = {2018},
doi = {10.1016/j.crma.2018.02.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2018.02.012/}
}
TY - JOUR AU - Banerjee, Abhishek TI - A topological nullstellensatz for tensor-triangulated categories JO - Comptes Rendus. Mathématique PY - 2018 SP - 365 EP - 375 VL - 356 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.02.012/ DO - 10.1016/j.crma.2018.02.012 LA - en ID - CRMATH_2018__356_4_365_0 ER -
%0 Journal Article %A Banerjee, Abhishek %T A topological nullstellensatz for tensor-triangulated categories %J Comptes Rendus. Mathématique %D 2018 %P 365-375 %V 356 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2018.02.012/ %R 10.1016/j.crma.2018.02.012 %G en %F CRMATH_2018__356_4_365_0
Banerjee, Abhishek. A topological nullstellensatz for tensor-triangulated categories. Comptes Rendus. Mathématique, Tome 356 (2018) no. 4, pp. 365-375. doi : 10.1016/j.crma.2018.02.012. http://www.numdam.org/articles/10.1016/j.crma.2018.02.012/
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