5 papers · 1 filter
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 mix…
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…
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…
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…