{"paper":{"title":"Perfectoid rings as Thom spectra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AT","authors_text":"Zhouhang Mao","submitted_at":"2020-03-19T11:37:25Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.08697","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.08697/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}