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| Format: | Preprint |
| Veröffentlicht: |
2020
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| Online-Zugang: | https://arxiv.org/abs/2003.08697 |
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| _version_ | 1866910591540527104 |
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| author | Mao, Zhouhang |
| author_facet | Mao, Zhouhang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_08697 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Perfectoid rings as Thom spectra Mao, Zhouhang Algebraic Topology Rings and Algebras 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. |
| title | Perfectoid rings as Thom spectra |
| topic | Algebraic Topology Rings and Algebras |
| url | https://arxiv.org/abs/2003.08697 |