A calculation of the perfectoidization of semiperfectoid rings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912125112287232 |
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| author | Ishizuka, Ryo |
| author_facet | Ishizuka, Ryo |
| contents | We show that perfectoidization can be (almost) calculated by using $p$-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidization and uniform completion, as well as the $p$-root closed property of integral perfectoid rings. Through this calculation, we establish a connection between a classical closure operation ``$p$-root closure'' used by Roberts in mixed characteristic commutative algebra and a more recent concept of ``perfectoidization'' introduced by Bhatt and Scholze in their theory of prismatic cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07916 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A calculation of the perfectoidization of semiperfectoid rings Ishizuka, Ryo Commutative Algebra Algebraic Geometry Number Theory We show that perfectoidization can be (almost) calculated by using $p$-root closure in certain cases, including the semiperfectoid case. To do this, we focus on the universality of perfectoidization and uniform completion, as well as the $p$-root closed property of integral perfectoid rings. Through this calculation, we establish a connection between a classical closure operation ``$p$-root closure'' used by Roberts in mixed characteristic commutative algebra and a more recent concept of ``perfectoidization'' introduced by Bhatt and Scholze in their theory of prismatic cohomology. |
| title | A calculation of the perfectoidization of semiperfectoid rings |
| topic | Commutative Algebra Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2305.07916 |