Geometric arcs and fundamental groups of rigid spaces-Reference-Cited by-同舟云学术

Geometric arcs and fundamental groups of rigid spaces

Published:2023-04-20 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Achinger Piotr¹^ORCID,Lara Marcin²^ORCID,Youcis Alex³^ORCID

Affiliation:

1. Institute of Mathematics of the Polish Academy of Sciences , Śniadeckich 8, 00-656 Warsaw , Poland

2. Institute of Mathematics of the Polish Academy of Sciences , Śniadeckich 8, 00-656 Warsaw ; and Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków , Poland

3. Institute of Mathematics of the Polish Academy of Sciences , Śniadeckich 8, 00-656 Warsaw , Poland ; and Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

Abstract

AbstractWe develop the notion of ageometric coveringof 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.

Funder

H2020 European Research Council

Deutsche Forschungsgemeinschaft

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2023-0013/pdf

Reference49 articles.

1. P. Achinger, M. Lara and A. Youcis, Variants of the de Jong fundamental group, preprint (2021), http://arxiv.org/abs/2203.11750.

2. P. Achinger, M. Lara and A. Youcis, Specialization for the pro-étale fundamental group, Compos. Math. 158 (2022), no. 8, 1713–1745.

3. Y. André, Period mappings and differential equations. From ℂ to C p \mathbb{C}_{p} , MSJ Mem. 12, Mathematical Society of Japan, Tokyo 2003.

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5. V. G. Berkovich, Étale cohomology for non-Archimedean analytic spaces, Publ. Math. Inst. Hautes Études Sci. 78 (1993), 5–161.

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