4 citations · 9 across the 4 of their papers we have counts for
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Perfectoid towers and their tilts : with an application to the étale cohomology groups of local log-regular rings
Shinnosuke Ishiro, Kei Nakazato, Kazuma Shimomoto
To initiate a systematic study on the applications of perfectoid methods to Noetherian rings, we introduce the notions of perfectoid towers and their tilts. We mainly show that the…
A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
Kei Nakazato, Kazuma Shimomoto
In this paper, we prove that a complete Noetherian local domain of mixed characteristic with perfect residue field has an integral extension that is an integrally closed, alm…
Finite étale extension of Tate rings and decompletion of perfectoid algebras
Kei Nakazato, Kazuma Shimomoto
In this paper, we examine the behavior of ideal-adic separatedness and completeness under certain ring extensions using trace map. Then we prove that adic completeness of a base ri…
Counter-examples to non-noetherian Elkik's approximation theorem
Kei Nakazato
Elkik established a remarkable theorem that can be applied for any noetherian henselian ring. For algebraic equations with a formal solution (restricted by some smoothness assumpti…