A nilpotent Whitehead theorem for TQ-homology of structured ring spectra

Michael Ching; John E. Harper

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arXiv · 1806.09901

A nilpotent Whitehead theorem for TQ-homology of structured ring spectra

Michael Ching·John E. Harper

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Abstract

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.

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Michael Ching, John E. Harper. 2018-06-26. A nilpotent Whitehead theorem for TQ-homology of structured ring spectra. https://arxiv.org/abs/1806.09901

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