Transchromatic phenomena in the equivariant slice spectral sequence

TL;DR

This paper establishes a transchromatic relationship between equivariant slice spectral sequences of different heights in Hill--Hopkins--Ravenel and Lubin--Tate theories, leading to new periodicity and vanishing results.

Contribution

It introduces a novel transchromatic phenomenon linking spectral sequences of different heights, advancing understanding of equivariant stable homotopy theories.

Findings

Proves a direct relationship between spectral sequences of height-h and height-h/2 theories.

Establishes periodicity results for these theories.

Demonstrates vanishing lines in the spectral sequences.

Abstract

In this paper, we prove a transchromatic phenomenon for Hill--Hopkins--Ravenel and Lubin--Tate theories. This establishes a direct relationship between the equivariant slice spectral sequences of height-$h$ and height-$(h/2)$ theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.