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arXiv · 2605.20598

The pro-\'etale fundamental group of singular schemes

Jiu-Kang Yu·Lei Zhang
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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.

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Jiu-Kang Yu, Lei Zhang. 2026-05-20. The pro-\'etale fundamental group of singular schemes. https://arxiv.org/abs/2605.20598

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