From the 1 of 9 linked papers with an AI index.
9 papers
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…
Algebraization of absolute perfectoidization via section rings
Ryo Ishizuka, Shou Yoshikawa
The paper develops a graded version of absolute perfectoidization for G‑graded adic rings and proves that the absolute perfectoidization of the structure sheaf of a projective‑type…
On Perfectoidizaiton 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 perfectoidizatio…
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…
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…