Homotopy pro-nilpotent structured ring spectra and topological Quillen localization

Yu Zhang

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arXiv · 1902.03500

Homotopy pro-nilpotent structured ring spectra and topological Quillen localization

Yu Zhang

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Abstract

The aim of this paper is to show that homotopy pro-nilpotent structured ring spectra are TQ-local, where structured ring spectra are described as algebras over a spectral operad O. Here, TQ is short for topological Quillen homology, which is weakly equivalent to O-algebra stabilization. An O-algebra is called homotopy pro-nilpotent if it is equivalent to a limit of nilpotent O-algebras. Our result provides new positive evidence to a conjecture by Francis-Gaisgory on Koszul duality for general operads. As an application, we simultaneously extend the previously known 0-connected and nilpotent TQ-Whitehead theorems to a homotopy pro-nilpotent TQ-Whitehead theorem.

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Yu Zhang. 2019-02-09. Homotopy pro-nilpotent structured ring spectra and topological Quillen localization. https://arxiv.org/abs/1902.03500

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