几何弧和刚性空间的基本群

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik Pub Date : 2021-05-11 DOI:10.1515/crelle-2023-0013

Piotr Achinger, Marcin Lara, Alex Youcis

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引用次数: 3

摘要

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。

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Geometric arcs and fundamental groups of rigid spaces

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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来源期刊

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.