Real Orientations of Lubin-Tate Spectra

TL;DR

This paper demonstrates that Lubin-Tate spectra at the prime 2 are Real oriented and Real Landweber exact, providing explicit computations of homotopy fixed point spectral sequences and analyzing the Hurewicz images across different heights.

Contribution

It establishes the Real orientation and Real Landweber exactness of Lubin-Tate spectra at prime 2 and computes the homotopy fixed point spectral sequences for these spectra.

Findings

Lubin-Tate spectra at prime 2 are Real oriented.

Explicit computation of homotopy fixed point spectral sequences.

Analysis of Hurewicz images in stable homotopy groups.

Abstract

We show that Lubin-Tate spectra at the prime $2$ are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height $n$, we compute the entire homotopy fixed point spectral sequence for $E_n$ with its $C_2$-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $C_2$-fixed points.