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September 2018 A nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectra
Michael Ching, John E. Harper
Tbilisi Math. J. 11(3): 69-79 (September 2018). DOI: 10.32513/tbilisi/1538532027

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.

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Michael Ching. John E. Harper. "A nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectra." Tbilisi Math. J. 11 (3) 69 - 79, September 2018. https://doi.org/10.32513/tbilisi/1538532027

Information

Received: 26 June 2018; Accepted: 11 July 2018; Published: September 2018
First available in Project Euclid: 3 October 2018

zbMATH: 07172276
MathSciNet: MR3954195
Digital Object Identifier: 10.32513/tbilisi/1538532027

Subjects:
Primary: 55P43
Secondary: 18G55, 55P48, 55U35

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

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Vol.11 • No. 3 • September 2018
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