Graded perfectoid rings
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910022767738880 |
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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 |