An application of the almost purity theorem to the homological conjectures

Abstract

The aim of this article is to establish the existence of big Cohen-Macaulay algebras in mixed characteristic in some special situation. The main result follows from the so-called almost purity theorem proved by Davis and Kedlaya.

to appear in Journal of Pure and Applied Algebra

References in corpus (5)

• Relative p-adic Hodge theory: Foundations
• The Theory of Witt Vectors
• On the Witt vector Frobenius
• Almost direct summands
• A note on the non-existence of small Cohen-Macaulay algebras

Cited by in corpus (7)

• Purity for the Brauer group
• Integral perfectoid big Cohen-Macaulay algebras via André's theorem
• On the Witt vectors of perfect rings in positive characteristic
• A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
• Counter-examples to non-noetherian Elkik's approximation theorem
• An embedding problem of Noetherian rings into the Witt vectors
• Singularities in mixed characteristic. The perfectoid approach