Regular rings and perfect(oid) algebras
Commutative Algebra
2018-09-11 v2
Abstract
We prove a -adic analog of Kunz's theorem: a -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 -adic Kunz's theorem where the flatness hypothesis is relaxed to almost flatness.
Cite
@article{arxiv.1803.03229,
title = {Regular rings and perfect(oid) algebras},
author = {Bhargav Bhatt and Srikanth B. Iyengar and Linquan Ma},
journal= {arXiv preprint arXiv:1803.03229},
year = {2018}
}
Comments
18 pages, add a secton to explain the almost version of the results