Ryo Ishizuka, Shou Yoshikawa
We construct and study a graded version of absolute perfectoidization for $G$-graded adic rings. As a main geometric application, we show that the absolute perfectoidization of the structure sheaf of a projective-type formal scheme admits an algebraization.
Ryo Ishizuka, Shou Yoshikawa
This paper contains 40 sections, 87 theorems, 276 equations.
Theorem A
Let $G$ be a torsion-free abelian group and let $p$ be a prime number. Let $R$ be a $G$-graded ring whose graded components $R_g$ are $p$-adically complete for all $g \in G$. Then there exists a $G$-graded $\mathbb{E}_{\infty}$-$R$-algebra called the absolute graded perfectoidization of $R$, satisfying the following properties: Moreover, it satisfies further properties analogous to those of the
