English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We systematically develop a theory of stratification in the context of tensortriangular geometry and apply it to classify the localizing tensor-ideals ofcertain categories of spectral $G$-Mackey functors for all finite groups $G$.Our theory of stratification is based on the approach of Stevenson which usesthe Balmer-Favi notion of big support for tensor-triangulated categories whoseBalmer spectrum is weakly noetherian. We clarify the role of thelocal-to-global principle and establish that the Balmer-Favi notion of supportprovides the universal approach to weakly noetherian stratification. Thisprovides a uniform new perspective on existing classifications in theliterature and clarifies the relation with the theory of Benson-Iyengar-Krause.Our systematic development of this approach to stratification, involving areduction to local categories and the ability to pass through finite \'{e}taleextensions, may be of independent interest. Moreover, we strengthen therelationship between stratification and the telescope conjecture. The startingpoint for our equivariant applications is the recent computation byPatchkoria-Sanders-Wimmer of the Balmer spectrum of the category of derivedMackey functors, which was found to capture precisely the height $0$ and height$\infty$ chromatic layers of the spectrum of the equivariant stable homotopycategory. We similarly study the Balmer spectrum of the category of$E(n)$-local spectral Mackey functors noting that it bijects onto the height$\le n$ chromatic layers of the spectrum of the equivariant stable homotopycategory; conjecturally the topologies coincide. Despite our incompleteknowledge of the topology of the Balmer spectrum, we are able to completelyclassify the localizing tensor-ideals of these categories of spectral Mackeyfunctors.

Stratification in tensor triangular geometry with applications to spectral Mackey functors