The Slice Spectral Sequence for certain $RO(C_{p^n})$-graded Suspensions of $H\underline{\mathbb Z}$

TL;DR

This paper investigates the slice filtration and spectral sequence for certain $RO(C_{p^n})$-graded suspensions of the Eilenberg-MacLane spectrum $Hrak{Z}$, aiming to understand how suspensions affect slices.

Contribution

It introduces a method to describe the slices of suspensions in terms of the original slices for $RO(C_{p^n})$-graded spectra, expanding the understanding of slice filtrations.

Findings

Analyzed the slice filtration for specific suspensions of $Hrak{Z}$.

Established a relationship between slices of suspensions and original slices.

Provided new tools for computing slices in equivariant stable homotopy theory.

Abstract

We study the slice filtration and associated spectral sequence for a family of $RO(C_{p^{n}})$-graded suspensions of the Eilenberg-MacLane spectrum for the constant Mackey functor $\underline{\mathbb Z}$. Since $H\underline{\mathbb Z}$ is the zero slice of the sphere spectrum, this begins an analysis of how one can describe the slices of a suspension in terms of the original slices.