Hill–Hopkins–Ravenel transchromatic phenomenon for equivariant slice spectral sequences

Let $E_h$ denote a height-$h$ Lubin–Tate theory equipped with the relevant finite-group action, and let the associated equivariant slice spectral sequence be the spectral sequence computing its fixed points. The slice spectral sequence at higher height is compared with those at lower height through regions in which the spectral sequences agree.

Hill–Hopkins–Ravenel transchromatic phenomenon. The slice spectral sequences of higher height theories contain isomorphism regions to the slice spectral sequences of lower height theories.

This conjecture proposes a systematic relationship between equivariant fixed-point computations at different chromatic heights. The paper proves a transchromatic isomorphism theorem in an important cyclic-group setting, but the general phenomenon asserted here is not established.