Another proof of the almost purity theorem for perfectoid valuation rings

DOI10.1016/j.jpaa.2021.106898zbMath1481.13009arXiv2012.13984OpenAlexW3198147144WikidataQ113870184 ScholiaQ113870184MaRDI QIDQ2078384

Shinnosuke Ishiro, Kazuma Shimomoto

Publication date: 28 February 2022

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.13984

zbMATH Keywords

valuation ringalmost purityFrobenius pull-back formulanormalized length

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Étale and flat extensions; Henselization; Artin approximation (13B40) Perfectoid spaces and mixed characteristic (14G45)

Cites Work

• Frobenius and valuation rings
• Almost ring theory
• Abhyankar's perfectoid lemma
• Perfectoid spaces
• Valuation rings are derived splinters
• Finite étale extensions of Tate rings and decompletion of perfectoid algebras
• -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES
• A Survey of Elliptic Cohomology
• Separable Algebras
• The Frobenius action on local cohomology modules in mixed characteristic
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