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