algebraic geometry

Algebraization of absolute perfectoidization via section rings

arXiv:2604.02682

summary

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 formal scheme can be algebraized.

Abstract

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 structure sheaf of a projective-type formal scheme admits an algebraization.

78 pages; some improvements in section 4 and 5

Topics & keywords

#perfectoid spaces#graded adic rings#absolute perfectoidization#algebraization#formal schemes#projective-type schemesabsolute perfectoidizationgraded adic ringssection ringsalgebraizationprojective formal schemeperfectoid geometry
Algebraization of absolute perfectoidization via section rings · wovepaper