Structured ring spectra and displays

Abstract

We combine Lurie’s generalization of the Hopkins–Miller theorem with work of Zink–Lau on displays to give a functorial construction of even-periodic $E_{\infty }$ ring spectra $E$, concentrated in chromatic layers $2$ and above, associated to certain $n\times n$ invertible matrices with coefficients in the Witt ring of ${\pi }_0\left(E\right)$. This is applied to examples related to Lubin–Tate and Johnson–Wilson spectra. We also give a Hopf algebroid presentation of the moduli of $p$–divisible groups of height greater than or equal to $2$.