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

TL;DR

This paper computes the topological Andre9-Quillen homology of Eilenberg-MacLane spectra like Ha9 and Ha9/p^n, extending previous work and using a Cartan-like approach for more efficient calculations.

Contribution

It provides new computations of topological Andre9-Quillen homology for specific spectra, refining and extending prior results with a shorter, Cartan-inspired method.

Findings

Computed TAQ homology for Ha9 and Ha9/p^n spectra

Extended calculations to Ha9 with reduced coefficients

Presented computations relative to the Ha9 base

Abstract

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 The case of $H\mathbb{F}_p$ was settled in an unpublished work of Basterra and Mandell, which was refined later by Brantner and Mathew in the context of spectral partition Lie algebras.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.