Graded perfectoid rings
Commutative Algebra
2026-02-17 v2 Algebraic Geometry
Number Theory
Abstract
We introduce and study graded perfectoid rings as graded analogues of Scholze's (integral) perfectoid rings. We establish a categorical equivalence between graded perfectoid rings and graded perfect prisms, extending the Bhatt-Scholze's correspondence to the graded setting. We also construct the initial graded perfectoid cover of any graded semiperfectoid rings and prove a graded version of Andr\'e's flatness lemma. These results lay the foundations for a graded theory of perfectoid rings.
Keywords
Cite
@article{arxiv.2511.02322,
title = {Graded perfectoid rings},
author = {Ryo Ishizuka and Shou Yoshikawa},
journal= {arXiv preprint arXiv:2511.02322},
year = {2026}
}
Comments
43 pages; added relations to prior works and refined the definition of graded perfectoid rings