半完美环的完美化计算

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal Pub Date : 2024-02-23 DOI:10.1017/nmj.2024.2

RYO ISHIZUKA

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引用次数: 0

摘要

我们证明，在某些情况下，包括在半完形情况下，完形化（几乎）可以用 p 根封闭来计算。为此，我们重点研究了完形化和均匀完形的普遍性，以及积分完形环的 p 根封闭性质。通过这一计算，我们建立了罗伯茨在混合特征交换代数中使用的经典闭合运算 "p 根闭合 "与巴特和肖尔茨在棱柱同调理论中引入的最新概念 "完形化 "之间的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A CALCULATION OF THE PERFECTOIDIZATION OF SEMIPERFECTOID RINGS

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 perfectoidizations and uniform completions, 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.

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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.