# Integral perfectoid big Cohen-Macaulay algebras via Andr\'e's theorem

## TL;DR

This paper proves that any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra, advancing the understanding of algebraic structures in mixed characteristic via André's construction.

## Contribution

It establishes the existence of integral perfectoid big Cohen-Macaulay algebras for all Noetherian local domains of mixed characteristic, using André's almost Cohen-Macaulay algebras.

## Key findings

- Any Noetherian local domain of mixed characteristic maps to an integral perfectoid big Cohen-Macaulay algebra.
- The absolute integral closure of a complete Noetherian local domain maps to such an algebra.
- The proof relies on André's construction of almost Cohen-Macaulay algebras.

## 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 Andr\'e. 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.