Perfectoid rings as Thom spectra

Zhouhang Mao

doi:10.1007/s00029-023-00851-0

Perfectoid rings as Thom spectra

Algebraic Topology 2024-09-09 v2 Rings and Algebras

Authors: 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.

Keywords

spectral sequences

Cite

@article{arxiv.2003.08697,
  title  = {Perfectoid rings as Thom spectra},
  author = {Zhouhang Mao},
  journal= {arXiv preprint arXiv:2003.08697},
  year   = {2024}
}

Comments

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

Perfectoid rings as Thom spectra

Abstract

Keywords

Cite

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