Transchromatic phenomena in the equivariant slice spectral sequence

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-$(h\mathrm{/}2)$ theories. As applications of this transchromatic phenomenon, we prove periodicity and vanishing line results for these theories.