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 establish a novel approach to computing $G$-equivariant cohomology for afinite group $G$, and demonstrate it in the case that $G = C_{p^n}$.  For any commutative ring spectrum $R$, we prove a symmetric monoidalreconstruction theorem for genuine $G$-$R$-modules, which records them in termsof their geometric fixedpoints as well as gluing maps involving their Tatecohomologies. This reconstruction theorem follows from a symmetric monoidalstratification (in the sense of \cite{AMR-strat}); here we identify the gluingfunctors of this stratification in terms of Tate cohomology.  Passing from genuine $G$-spectra to genuine $G$-$\mathbb{Z}$-modules (a.k.a.derived Mackey functors) provides a convenient intermediate category forcalculating equivariant cohomology. Indeed, as $\mathbb{Z}$-linear Tatecohomology is far simpler than $\mathbb{S}$-linear Tate cohomology, the abovereconstruction theorem gives a particularly simple algebraic description ofgenuine $G$-$\mathbb{Z}$-modules. We apply this in the case that $G = C_{p^n}$for an odd prime $p$, computing the Picard group of genuine$G$-$\mathbb{Z}$-modules (and therefore that of genuine $G$-spectra) as well asthe $RO(G)$-graded and Picard-graded $G$-equivariant cohomology of a point.

Derived Mackey functors and $C_{p^n}$-equivariant cohomology