On a nilpotence conjecture of J.P. May

We prove a conjecture of J.P. May concerning the nilpotence of elements in ring spectra with power operations, i.e., \(H_\infty\)-ring spectra. Using an explicit nilpotence bound on the torsion elements in \(K(n)\)-local \(H_\infty\)-algebras over \(E_n\), we reduce the conjecture to the nilpotence...

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Bibliographic Details
Published in:arXiv.org 2015-05
Main Authors: Mathew, Akhil, Naumann, Niko, Noel, Justin
Format: Article
Language:English
Subjects:
Ring structures
Spectra
Online Access:Get full text
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Summary:We prove a conjecture of J.P. May concerning the nilpotence of elements in ring spectra with power operations, i.e., \(H_\infty\)-ring spectra. Using an explicit nilpotence bound on the torsion elements in \(K(n)\)-local \(H_\infty\)-algebras over \(E_n\), we reduce the conjecture to the nilpotence theorem of Devinatz, Hopkins, and Smith. As corollaries we obtain nilpotence results in various bordism rings including \(M\mathit{Spin}_*\) and \(M\mathit{String}_*\), results about the behavior of the Adams spectral sequence for \(E_\infty\)-ring spectra, and the non-existence of \(E_\infty\)-ring structures on certain complex oriented ring spectra.
ISSN:2331-8422
DOI:10.48550/arxiv.1403.2023