1 citations · 1 across the 10 of their papers we have counts for
10 papers
Hodge--Tate splitting and Akizuki--Nakano vanishing in positive characteristic
Ryo Ishizuka, Shou Yoshikawa
We introduce the notion of Hodge--Tate splitting for schemes in positive characteristic. For a smooth variety over a perfect field of characteristic , we say that $X…
Homological Detection by Perfectoid Algebras
Mohsen Asgharzadeh, Ryo Ishizuka
We first establish estimates for the projective and injective dimensions for quotients of perfectoid algebras by radical ideals. As applications, we obtain homological characteriza…
On Perfectoidization of Finite Algebras over a Perfectoid Ring
Ryo Ishizuka, Léo Navarro Chafloque
We study general properties of the perfectoidization of finite algebras over a perfectoid ring, which helps to understand some precise and explicit descriptions. For example, we pr…
Decomposition Theorem for Perfectoid Rings along General Ideals
Ryo Ishizuka, Léo Navarro Chafloque
Using André's lemma and the excision square for perfectoidization coming from -complete arc descent, we prove new structural results about perfectoid rings and perfectoidization…
A local-global correspondence for perfectoid purity
Ryo Ishizuka, Shou Yoshikawa
We introduce (lim-)perfectoid splitting, which is a global variant of (lim-)perfectoid purity. Our main result establishes a correspondence between the lim-perfectoid splitting of…
Algebraization of absolute perfectoidization via section rings
Ryo Ishizuka, Shou Yoshikawa
We construct and study a graded version of absolute perfectoidization for -graded adic rings. As a main geometric application, we show that the absolute perfectoidization of the…
Derived graded modules
Ryo Ishizuka, Shou Yoshikawa
We introduce the notion of the -category of (complete) derived -graded modules over a -graded ring for a torsion-free abelian group , and we study its foundati…
Graded perfectoid rings
Ryo Ishizuka, Shou Yoshikawa
We introduce and study graded perfectoid rings as graded analogues of Scholze's (integral) perfectoid rings. We establish a categorical equivalence between graded perfectoid rings…
Perfectoid towers generated from prisms
Ryo Ishizuka
We present a unified construction of perfectoid towers from specific prisms which covers all the previous constructions of (p-torsion-free) perfectoid towers. By virtue of the cons…
Prismatic Kunz's theorem
Ryo Ishizuka, Kei Nakazato
In this paper, we prove "prismatic Kunz's theorem" which states that a complete Noetherian local ring of residue characteristic is a regular local ring if and only if the F…