From the 1 of 6 linked papers with an AI index.
6 papers
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…
Tight closure of ideals on Witt rings
Shou Yoshikawa
In this paper, we introduce the notions of tight closure of ideals on Witt rings and quasi-tightly closedness of system of parameters. By using the notions, we obtain a characteriz…
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…
Perfectoid splitting and global -regularity for smooth hypersurfaces
Shou Yoshikawa
In this paper, we prove that smooth Calabi--Yau hypersurfaces of degree over complete unramified discrete valuation rings with residue characteristic are perfectoid split i…
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…
On the boundedness of -algebra homomorphisms between -affinoid algebras
Shou Yoshikawa
Let be a complete non-archimedean non-trivial valued field. In this paper, we investigate whether every -algebra homomorphism between -affinoid algebras is automatically…