The Slice Spectral Sequence of a 𝐶₄-Equivariant Height-4 Lubin–Tate Theory

Abstract

We completely compute the slice spectral sequence of the C 4 C_4 -spectrum B P ( ( C 4 ) ) ⟨ 2 ⟩ BP^{(\!(C_4)\!)}\langle 2 \rangle . This spectrum provides a model for a height-4 Lubin–Tate theory with a C 4 C_4 -action induced from the Goerss–Hopkins–Miller theorem. In particular, our computation shows that E 4 h C 12 E_4^{hC_{12}} is 384-periodic.