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Cosupport in tensor triangular geometry
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We develop a theory of cosupport and costratification in tensor triangular geometry. We study the geometric relationship between support and cosupport, provide a conceptual foundation for cosupport as categorically dual to support, and discover surprising relations between the theory of costratification and the theory of stratification. We prove that many categories in algebra, topology and geometry are costratified by developing and applying descent techniques. An overarching theme is that cosupport is relevant for diverse questions in tensor triangular geometry and that a full understanding of a category requires knowledge of both its support and its cosupport.
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Cohen's theorem in tensor triangular geometry
For essentially small tensor triangulated categories with weakly Noetherian spectrum, every radical ideal is finitely generated if and only if the Balmer spectrum is finite.
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