The pro-\'etale fundamental group of singular schemes
Algebraic Geometry
2026-05-21 v1 Algebraic Topology
Number Theory
Abstract
We compute the pro-\'etale fundamental group of a connected Nagata J-2 scheme in terms of the \'etale fundamental groups of the normalizations of its irreducible components and a discrete free group. The result generalizes a formula of E. Lavanda for semi-stable curves and relies on a combination of proper descent techniques for \'etale morphisms and a combinatorial van Kampen construction for Noohi groups. As a by-product we characterize when a continuous representation of the pro-\'etale fundamental group factors through a discrete quotient.
Cite
@article{arxiv.2605.20598,
title = {The pro-\'etale fundamental group of singular schemes},
author = {Jiu-Kang Yu and Lei Zhang},
journal= {arXiv preprint arXiv:2605.20598},
year = {2026}
}
Comments
With an appendix by Marcin Lara