Structured ring spectra and displays

TL;DR

This paper constructs new even-periodic commutative ring spectra using displays and Lurie's theorem, linking algebraic structures to chromatic homotopy theory, and provides a presentation of moduli of p-divisible groups.

Contribution

It introduces a functorial method to build ring spectra from invertible matrices over Witt rings, extending the connection between displays and chromatic layers.

Findings

Construction of ring spectra related to Lubin-Tate and Johnson-Wilson spectra

A Hopf algebroid presentation of moduli of p-divisible groups

Extension of the Hopkins-Miller theorem using 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 commutative ring spectra, concentrated in chromatic layers 2 and above, associated to certain n by n invertible matrices with coefficients in Witt rings. 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.