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arXiv · 2003.08697

Perfectoid rings as Thom spectra

Zhouhang Mao
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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.

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Zhouhang Mao. 2020-03-19. Perfectoid rings as Thom spectra. https://doi.org/10.1007/s00029-023-00851-0

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