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 much larger class of covering spaces than that studied previously by de Jong. Geometric coverings of X are closed under disjoint unions and are \'etale 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," making it similar to geometric coverings of schemes studied by Bhatt and Scholze as well as semicoverings of topological spaces introduced by Brazas.
Cite
@article{arxiv.2105.05184,
title = {Geometric arcs and fundamental groups of rigid spaces},
author = {Piotr Achinger and Marcin Lara and Alex Youcis},
journal= {arXiv preprint arXiv:2105.05184},
year = {2022}
}
Comments
38 pages. The previous version has been split into two parts. Part II, titled "Variants of the de Jong fundamental group", is available as a separate arXiv submission arXiv:2203.11750