A nilpotent Whitehead theorem for TQhomology
of structured ring spectra
M. Ching, J. E. Harper
The aim of this short paper is to prove a TQWhitehead 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 TQhomology analog for structured ring spectra of Dror's generalized Whitehead theorem for topological spaces;
here TQhomology is short for topological Quillen homology.
We also prove retract theorems for the TQcompletion and homotopy completion of nilpotent structured ring spectra.
Tbilisi Mathematical Journal, Vol. 11(3) (2018), pp. 6979
