Strict units of commutative ring spectra

Abstract

We provide computational tools to calculate the strict units of commutative ring spectra. We describe the Goerss-Hopkins-Miller spectral sequence for computing strict units of $E_\infty$-$H\mathbb{F}_p$-algebras, and use it to compute the strict units of polynomial and truncated polynomial rings, whose Postnikov towers we also analyze. We then sketch the calculation of the strict units of other rings, such as $S^0$, using the symmetric product of spheres filtration and transfers.