Perfectoid rings as Thom spectra
Abstract
The Hopkins-Mahowald theorem realizes the Eilenberg-Maclane spectra H Fp as Thom spectra for all primes p∈ 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.
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