vix.ing · top · new · best · stats · spec

Costratification and actions of tensor-triangulated categories

2022/11/08 by Verasdanis, Charalampos
#18F99 #18G80 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.04139

Abstract

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 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.

Related