$\mathbb{E}_\infty$ automorphisms of motivic Morava $E$-theories

TL;DR

This paper demonstrates that motivic Morava $E$-theories always possess $E_ fty$ structures, but also reveals the existence of exotic automorphisms beyond the classical Morava stabilizer group, using obstruction theory.

Contribution

It applies Goerss--Hopkins obstruction theory to motivic spectra to establish the existence of $E_ fty$ structures and identifies exotic automorphisms not derived from known groups.

Findings

Motivic Morava $E$-theories admit $E_ fty$ structures.

Existence of exotic automorphisms beyond the Morava stabilizer group.

Application of obstruction theory to motivic spectra.

Abstract

We apply Goerss--Hopkins obstruction theory for motivic spectra to study the motivic Morava $E$-theories. We find that they always admit $\mathbb{E}_\infty$ structures, but that these may admit "exotic" $\mathbb{E}_\infty$ automorphisms not coming from the usual Morava stabilizer group.