# Stratification in tensor triangular geometry with applications to spectral Mackey functors

@inproceedings{Barthel2021StratificationIT, title={Stratification in tensor triangular geometry with applications to spectral Mackey functors}, author={Tobias Barthel and Drew Heard and Beren Sanders}, year={2021} }

We systematically develop a theory of stratification in the context of tensor triangular geometry and apply it to classify the localizing tensorideals of certain categories of spectral G-Mackey functors for all finite groups G. Our theory of stratification is based on the approach of Stevenson which uses the Balmer–Favi notion of big support for tensor-triangulated categories whose Balmer spectrum is weakly noetherian. We clarify the role of the local-toglobal principle and establish that the…

## 6 Citations

### Stratifying integral representations of finite groups

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We classify the localizing tensor ideals of the integral stable module category for any finite group G. This results in a generic classification of Z[G]-lattices of finite and infinite rank and…

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### Stratification and the comparison between homological and tensor triangular support

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We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine whether a class is…

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