A nilpotent Whitehead theorem for TQ-homology of structured ring spectraM. Ching, J. E. HarperThe 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 |