Geometric arcs and fundamental groups of rigid spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-11 DOI:10.1515/crelle-2023-0013

Piotr Achinger, Marcin Lara, Alex Youcis

引用次数: 3

Abstract

Abstract We develop the notion of a geometric covering of a rigid space 𝑋, which yields a larger class of covering spaces than that studied previously by de Jong. Geometric coverings are closed under disjoint unions and are étale local on 𝑋. If 𝑋 is connected, its geometric coverings form a tame infinite Galois category and hence are classified by a topological group. The definition is based on the property of lifting of “geometric arcs” and is meant to be an analogue of the notion developed for schemes by Bhatt and Scholze.

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几何弧和刚性空间的基本群

我们发展了刚性空间𝑋的几何覆盖的概念，它产生了比de Jong先前研究的更大的覆盖空间类别。几何覆盖物在不连接的连接下是闭合的，并且在𝑋上是局部的。如果𝑋是连通的，它的几何覆盖形成了一个驯服的无限伽罗瓦范畴，因此被一个拓扑群分类。这个定义是基于“几何弧”的提升性质，是对Bhatt和Scholze为方案开发的概念的类比。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.