Perfectoid rings as Thom spectra

Abstract

The Hopkins-Mahowald theorem realizes the Eilenberg-Maclane spectra $H{\mathbb{F}}_p$ as Thom spectra for all primes $p\in {\mathbb{N}}_{>0}$. In this article, we record a known proof of a generalization of Hopkins-Mahowald theorem, realizing $Hk$ as Thom spectra for perfect rings $k$, and we provide a further generalization by realizing $HR$ as Thom spectra for perfectoid rings $R$. We also discuss even further generalizations to prisms $(A,I)$ and indicates how to adapt our proofs to Breuil-Kisin case.

Minor updates (including some numbering and some typesetting change). Two references about the iterated loop space of the 3-sphere are added

Cited by in corpus (1)

• Filtered formal groups, Cartier duality, and derived algebraic geometry