A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
arXiv:2002.03512 · doi:10.1017/nmj.2023.23
Abstract
In this paper, we prove that a complete Noetherian local domain of mixed characteristic 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 . 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.
arXiv commentTo appear in Nagoya Math. J
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