A nilpotent Whitehead theorem for TQ-homology
of structured ring spectra
M. Ching, J. E. Harper
The aim of this short paper is to prove a TQ-Whitehead theorem for nilpotent structured ring spectra.
We work in the framework of symmetric spectra and algebras over operads in modules over a commutative ring spectrum.
Our main result can be thought of as a TQ-homology analog for structured ring spectra of Dror's generalized Whitehead theorem for topological spaces;
here TQ-homology is short for topological Quillen homology.
We also prove retract theorems for the TQ-completion and homotopy completion of nilpotent structured ring spectra.
Tbilisi Mathematical Journal, Vol. 11(3) (2018), pp. 69-79