Topological Andr\'e-Quillen homology for cellular commutative $S$-algebras

TL;DR

This paper studies topological André-Quillen homology for CW $S$-algebras, applying it to classify minimal atomic $p$-local $S$-algebras and providing new examples, extending previous work on $p$-local spectra.

Contribution

It develops the homology theory on CW $S$-algebras and generalizes results on minimal atomic $p$-local $S$-algebras, introducing new examples.

Findings

Classification of minimal atomic $p$-local $S$-algebras

Extension of results from $p$-local spectra to $S$-algebras

New examples of minimal atomic $S$-algebras

Abstract

Topological Andr\'e-Quillen homology for commutative $S$-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this paper we discuss it as a homology theory on CW $S$-algebras and apply it to obtain results on minimal atomic $p$-local $S$-algebras which generalise those of Baker and May for $p$-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic $S$-algebras.