3 citations · 7 across the 6 of their papers we have counts for
7 papers
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…
Log-regularity of monoid algebras
Shinnosuke Ishiro
Local log-regular rings are Cohen-Macaulay local domains introduced by Kazuya Kato to expand the theory of toric varieties without a base. In this note, we show that local rings of…
Local log-regular rings vs. toric rings
Shinnosuke Ishiro
Local log-regular rings are a certain class of Cohen-Macaulay local rings that are treated in logarithmic geometry. Our paper aims to provide purely commutative ring theoretic proo…
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…
Surjectivity of some local cohomology map and the second vanishing theorem
Mohsen Asgharzadeh, Shinnosuke Ishiro, Kazuma Shimomoto
The second vanishing theorem has a long history in the theory of local cohomology modules, which connects the vanishing of a complete regular local ring with a topological property…
Another proof of the almost purity theorem for perfectoid valuation rings
Shinnosuke Ishiro, Kazuma Shimomoto
The almost purity theorem is central to the geometry of perfectoid spaces and has numerous applications in algebra and geometry. This result is known to have several different proo…