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Description

Let $R$ be a perfectoid ring. Hesselholt and Bhatt-Morrow-Scholze have identified the Postnikov filtration on $\mathrm{THH}(R;\mathbb Z_p)$: it is concentrated in even degrees, generated by powers of the Bökstedt generator $\sigma$, generalizing classical Bökstedt periodicity for $R=\mathbb F_p$. We study an equivariant generalization, the \emph{regular slice filtration}, on $\mathrm{THH}(R;\mathbb Z_p)$. The slice filtration is again concentrated in even degrees, generated by $RO(\mathbb T)$-graded classes which can loosely be thought of as \emph{norms} of $\sigma$. The slices themselves are $RO(\mathbb T)$-graded suspensions of certain Mackey functors. When $R$ is $p$-torsionfree, the slice spectral sequence is concentrated in even degrees and collapses on the $E^2$ page.