Support and vanishing for non-Noetherian rings and tensor triangulated categories

Sanders, William T.

doi:10.48550/arxiv.1710.10199

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2023

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References 15 publications

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“…A general approach to extending the Balmer-Favi support to points which are not weakly visible is considered by William Sanders [San17] and has been further developed in recent work of Changhan Zou [Zou23]. The inclusion-preserving function (7.2) is always surjective by Corollary 5.10, so costratification amounts to its injectivity.…”

Section: Remarkmentioning

confidence: 99%

Cosupport in tensor triangular geometry

Barthel¹,

Castellana²,

Heard³

et al. 2023

Preprint

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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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Section: Remarkmentioning

confidence: 99%