Integral perfectoid big Cohen-Macaulay algebras via André's theorem

Abstract

The main result of this article is to prove that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra. The proof of this result is based on the construction of almost Cohen-Macaulay algebras in mixed characteristic due to Yves André. Moreover, we prove that the absolute integral closure of a complete Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra.

Final version: to appear in Math. Annalen

References in corpus (2)

• Extended plus closure in complete local rings
• Regular rings and perfect(oid) algebras

Cited by in corpus (5)

• Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
• Cohen-Macaulayness of absolute integral closures
• A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
• Finite étale extension of Tate rings and decompletion of perfectoid algebras
• Singularities in mixed characteristic. The perfectoid approach