8 papers
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…
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 cohom…
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…
Quasi-canonical lifting of projective varieties in positive characteristic
Ryo Ishizuka, Kazuma Shimomoto
The main aim of this article is to give new classes of smooth projective varieties over characteristic that admit flat liftings over the Witt vectors together with additional…
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…
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…