A study of perfectoid rings via Galois cohomology

2025/05/03 by Kinouchi, Ryo, Shimomoto, Kazuma · 2 citations
#Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.01922

Abstract

In his foundational study of p-adic Hodge theory, Faltings introduced the method of almost étale extensions to establish fundmental comparison results of various p-adic cohomology theories. Scholze introduced the tilting operations to study algebraic objects arising from p-adic Hodge theory in mixed characteristic via the Frobenius map. In this article, we prove a few results which clarify certain ring-theoretic or homological properties of the tilt of an extension between perfectoid rings treated in the construction of big Cohen-Macaulay algebras.

Citations

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• Almost ring theory

Cited by

• δ-rings, perfectoid towers, and lim Cohen-Macaulay sequences
• On complete integral closedness of the p-adic completion of absolute integral closure

Related

• Tilting Correspondences of Perfectoid Rings
• Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings
• Perfectoidness via Sen Theory and Applications to Shimura Varieties
• Cohomological Descent for Faltings' p-adic Hodge Theory and Applications
• A mixed characteristic analogue of the perfection of rings and its almost Cohen-Macaulay property