On a nilpotence conjecture of J.P. May

Abstract

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 $M{Spin}_{\ast }$ and $M{String}_{\ast }$, 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.

17 pages. To appear in Journal of Topology

References in corpus (1)

• A simple universal property of Thom ring spectra

Cited by in corpus (6)

• The Picard group of topological modular forms via descent theory
• A simple universal property of Thom ring spectra
• Eilenberg-MacLane spectra as equivariant Thom spectra
• Exotic Multiplications on Periodic Complex Bordism
• Towards topological Hochschild homology of Johnson-Wilson spectra
• Higher chromatic Thom spectra via unstable homotopy theory