2018/03/08 by Bhargav Bhatt, Srikanth B. Iyengar, Bhatt, Bhargav +3 · 3 citations
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1803.03229
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.