A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras

Abstract

In this paper, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen-Macaulay domain such that the Frobenius map is surjective modulo $p$. This result is seen as a mixed characteristic analogue of the fact that the perfect closure of a complete local domain in positive characteristic is almost Cohen-Macaulay. To this aim, we carry out a detailed study of decompletion of perfectoid rings and establish the Witt-perfect (decompleted) version of André's perfectoid Abhyankar's lemma and Riemann's extension theorem.

To appear in Nagoya Math. J

References in corpus (3)

• On the Witt vector Frobenius
• Coherence of absolute integral closures
• Closure operations in complete local rings of mixed characteristic

Cited by in corpus (1)

• A calculation of the perfectoidization of semiperfectoid rings