7 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…
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…
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…
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…
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…