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.