Graded perfectoid rings

Fuente: arXiv
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Main Authors: Ishizuka, Ryo, Yoshikawa, Shou
Format: Preprint
Published: 2025
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author Ishizuka, Ryo
Yoshikawa, Shou
author_facet Ishizuka, Ryo
Yoshikawa, Shou
contents 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 André's flatness lemma. These results lay the foundations for a graded theory of perfectoid rings.
format Preprint
id arxiv_https___arxiv_org_abs_2511_02322
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Graded perfectoid rings
Ishizuka, Ryo
Yoshikawa, Shou
Commutative Algebra
Algebraic Geometry
Number Theory
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 André's flatness lemma. These results lay the foundations for a graded theory of perfectoid rings.
title Graded perfectoid rings
topic Commutative Algebra
Algebraic Geometry
Number Theory
url https://arxiv.org/abs/2511.02322