17 citations · 127 across the 33 of their papers we have counts for
31 papers · 1 filter
An application of Fontaine's monoidal maps to perfectoid towers
Kazuki Hayashi, Shinnosuke Ishiro, Kazuma Shimomoto
To connect arithmetic and ring-theoretic properties of rings of mixed characteristic with those of positive characteristic, we introduce monoidal maps for perfectoid towers. Using…
δ-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Shinnosuke Ishiro, Kazuma Shimomoto
The aim of this article is to study basic structures and interrelations of -rings, perfectoid towers, and lim Cohen--Macaulay sequences over Noetherian rings in positive or mixe…
A study of perfectoid rings via Galois cohomology
Ryo Kinouchi, Kazuma Shimomoto
In his foundational study of -adic Hodge theory, Faltings introduced the method of almost étale extensions to establish fundamental comparison results of various -adic cohomo…
Hyperplane sections of non-standard graded rings
Kazuma Shimomoto
The purpose of this paper is to explain a method on the generalization of the Bertini-type theorem on standard graded rings to the non-standard graded case of certain type.
Matijevic-Roberts type theorems, Rees rings and associated graded rings
Jun Horiuchi, Kazuma Shimomoto
The aim of this article is to investigate interrelated structures lying among three notable problems in commutative algebra. These are Lifting problem, Ascent/descent along associa…
A mixed characteristic analogue of the perfection of rings and its almost Cohen-Macaulay property
Ryo Ishizuka, Kazuma Shimomoto
Over a complete Noetherian local domain of mixed characteristic with perfect residue field, we construct a perfectoid ring which is similar to an explicit representation of a perfe…