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E-infinity-Descendability for Morava E-Theory

Author: Wei Yang · Added: September 5, 2026

Article date: September 5, 2026.

Abstract

Let $E_n$ be the Morava theory of the Honda formal group over $\mathbf{F}_{p^n}$ . We prove that $E_n^{hG}\to E_n$ is $\mathbb{E}_\infty$ -descendable for every closed subgroup $G$ of the extended Morava stabilizer group, both in $K(n)$ -local spectra and in ordinary spectra. In particular, this holds for $L_{K(n)}\mathbb{S}\to E_n$ . For groups of finite $p$ -cohomological dimension, the algebra retraction comes from a section after relative $p$ -finite completion of a finite join. Finite cyclic quotients are treated by a unital arity obstruction tower, whose possible obstructions are restricted to the arities $p,p^2,\ldots,p^n$ by chromatic vanishing for partition spectra.