An Atiyah–Hirzebruch spectral sequence for topological André–Quillen homology

We show how topological André–Quillen homology can be related to the usual algebraic André–Quillen homology. To this end we construct an Atiyah–Hirzebruch spectral sequence starting with the algebraic version and converging to the topological theory. This determines topological André–Quillen homology in classical cases of étale and smooth algebras.