Costratification and actions of tensor-triangulated categories

We develop the theory of costratification in the setting of relative tensor-triangular geometry, in the sense of Stevenson, providing a unified approach to classification results of Neeman and Benson--Iyengar--Krause, while laying the foundations for future applications. In addition, we introduce an...

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Bibliographic Details
Published in:arXiv.org 2023-11
Main Author: Verasdanis, Charalampos
Format: Article
Language:English
Subjects:
Mathematical analysis
Sheaves
Tensors
Online Access:Get full text
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Summary:We develop the theory of costratification in the setting of relative tensor-triangular geometry, in the sense of Stevenson, providing a unified approach to classification results of Neeman and Benson--Iyengar--Krause, while laying the foundations for future applications. In addition, we introduce and study prime localizing submodules and prime colocalizing \(\mathrm{hom}\)-submodules, in the first case, generalizing objectwise-prime localizing tensor-ideals. We apply our results to show that the derived category of quasi-coherent sheaves over a noetherian separated scheme is costratified.
ISSN:2331-8422