In locally cohomologically stratified tensor triangular categories with noetherian spectrum, the dualizable localizing ideals are exactly the localizing ideals supported on convex subsets of the Balmer spectrum.
Stratifying integral representations via equivariant homotopy theory
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abstract
We prove that the derived category of $R$-linear representations of a finite group $G$ is stratified for any regular commutative ring $R$. As an application, we obtain a classification of localizing tensor ideals of ordinary $R$-linear $G$-representations whose underlying $R$-module is projective.
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Convexity in tensor triangular geometry
In locally cohomologically stratified tensor triangular categories with noetherian spectrum, the dualizable localizing ideals are exactly the localizing ideals supported on convex subsets of the Balmer spectrum.