Models of Lubin-Tate spectra via Real bordism theory

TL;DR

This paper constructs equivariant models of Lubin-Tate spectra with cyclic group actions using Real bordism theory, providing explicit formulas and analyzing formal group law heights in an equivariant setting.

Contribution

It introduces new $C_{2^n}$-equivariant models of Lubin-Tate spectra based on Real bordism, with explicit formulas for group actions and formal group law heights.

Findings

Constructed $C_{2^n}$-equivariant models of Lubin-Tate spectra.

Derived explicit formulas for $C_{2^n}$-actions on coefficient rings.

Analyzed the height of formal group laws in the equivariant context.

Abstract

We study certain formal group laws equipped with an action of the cyclic group of order a power of $2$. We construct $C_{2^n}$-equivariant Real oriented models of Lubin-Tate spectra $E_h$ at heights $h=2^{n-1}m$ and give explicit formulas of the $C_{2^n}$-action on their coefficient rings. Our construction utilizes equivariant formal group laws associated with the norms of the Real bordism theory $MU_{\mathbb{R}}$, and our work examines the height of the formal group laws of the Hill-Hopkins-Ravenel norms of $MU_{\mathbb{R}}$.