Strong generators in tensor triangulated categories
classification
🧮 math.CT
math.AC
keywords
tensorcategorygeneratorsnon-zeroproperstrongthicktriangulated
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We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over a commutative ring without non-trivial idempotents has no proper non-zero thick subcategories that are strongly generated.
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