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 study the tensor-triangular geometry of the category of rational$G$-spectra for a compact Lie group $G$. In particular, we prove that thiscategory can be naturally decomposed into local factors supported on individualsubgroups, each of which admits an algebraic model. This is an important stepand strong evidence towards the third author's conjecture that the category ofrational $G$-spectra admits an algebraic model for all compact Lie groups.  To facilitate these results, we relate topological properties of theassociated Balmer spectrum to structural features of the group $G$ and thecategory of rational $G$-spectra. A key ingredient is our presentation of thespectrum as a Priestley space, separating the Hausdorff topology on conjugacyclasses of closed subgroups of $G$ from the cotoral ordering. We use this toprove that the telescope conjecture holds in general for rational $G$-spectra,and we determine exactly when the Balmer spectrum is Noetherian. In order toconstruct the desired decomposition of the category, we develop a generaltheory of `prismatic decompositions' of rigidly-compactly generatedtensor-triangulated categories, which in favourable cases gives a series ofrecollements for reconstructing the category from local factors over individualpoints of the spectrum.

Prismatic decompositions and rational $G$-spectra