On Topological Andr\'e-Quillen homology of Eilenberg-MacLane spectra

Based on the work of Dundas, Lindenstrauss and Richter we compute the topological Andr\'e-Quillen homology with reduced coefficients for Eilenberg-MacLane spectra such as $H\mathbb{Z}$ and $H\mathbb{Z}/p^n$. The case of $H\mathbb{F}_p$ was settled in an unpublished work of Basterra and Mandell, which was refined later by Brantner and Mathew in the context of spectral partition Lie algebras. Our approach is similar to Cartan's calculation of the Steenrod algebra, and eventually shorter. We also present some computations relative to the $H\mathbb{Z}$ base.