The pro-étale fundamental group of singular schemes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913147316600832 |
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| author | Yu, Jiu-Kang Zhang, Lei |
| author_facet | Yu, Jiu-Kang Zhang, Lei |
| contents | We compute the pro-étale fundamental group of a connected Nagata J-2 scheme in terms of the étale 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 étale morphisms and a combinatorial van Kampen construction for Noohi groups. As a by-product we characterize when a continuous representation of the pro-étale fundamental group factors through a discrete quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20598 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The pro-étale fundamental group of singular schemes Yu, Jiu-Kang Zhang, Lei Algebraic Geometry Algebraic Topology Number Theory We compute the pro-étale fundamental group of a connected Nagata J-2 scheme in terms of the étale 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 étale morphisms and a combinatorial van Kampen construction for Noohi groups. As a by-product we characterize when a continuous representation of the pro-étale fundamental group factors through a discrete quotient. |
| title | The pro-étale fundamental group of singular schemes |
| topic | Algebraic Geometry Algebraic Topology Number Theory |
| url | https://arxiv.org/abs/2605.20598 |