Integral perfectoid big Cohen–Macaulay algebras via André’s theorem

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,...

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Bibliographic Details
Published in:Mathematische annalen 2018-12, Vol.372 (3-4), p.1167-1188
Main Author: Shimomoto, Kazuma
Format: Article
Language:English
Subjects:
Algebra
Integrals
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-018-1704-x