Cosupport in tensor triangular geometry

Tobias Barthel; Natalia Castellana; Drew Heard; Beren Sanders

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arXiv · 2303.13480

Cosupport in tensor triangular geometry

Tobias Barthel·Natalia Castellana·Drew Heard·Beren Sanders

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Abstract

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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BibTeX RIS

Tobias Barthel, Natalia Castellana, Drew Heard, Beren Sanders. 2023-03-23. Cosupport in tensor triangular geometry. https://arxiv.org/abs/2303.13480

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