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arXiv · 1803.03229

Regular rings and perfect(oid) algebras

Bhargav Bhatt·Srikanth B. Iyengar·Linquan Ma
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Abstract

We prove a $p$-adic analog of Kunz's theorem: a $p$-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a more precise statement on detecting finiteness of projective dimension of finitely generated modules over noetherian rings via maps to perfectoid rings. We also establish a version of the $p$-adic Kunz's theorem where the flatness hypothesis is relaxed to almost flatness.

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Bhargav Bhatt, Srikanth B. Iyengar, Linquan Ma. 2018-03-08. Regular rings and perfect(oid) algebras. https://arxiv.org/abs/1803.03229

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