Tbilisi Mathematical Journal

A nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectra

Michael Ching and John E. Harper

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Abstract

The aim of this short paper is to prove a $\mathsf{TQ}$-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 $\mathsf{TQ}$-homology analog for structured ring spectra of Dror's generalized Whitehead theorem for topological spaces; here $\mathsf{TQ}$-homology is short for topological Quillen homology. We also prove retract theorems for the $\mathsf{TQ}$-completion and homotopy completion of nilpotent structured ring spectra.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 3 (2018), 69-79.

Dates
Received: 26 June 2018
Accepted: 11 July 2018
First available in Project Euclid: 3 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1538532027

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)
Secondary: 55U35: Abstract and axiomatic homotopy theory 55P48: Loop space machines, operads [See also 18D50] 18G55: Homotopical algebra

Keywords
Symmetric spectra structured ring spectra calculus of functors operads topological Quillen homology

Citation

Ching, Michael; Harper, John E. A nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectra. Tbilisi Math. J. 11 (2018), no. 3, 69--79. https://projecteuclid.org/euclid.tbilisi/1538532027


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