On branched coverings of the projective line over the integers

[2608.15057] On branched coverings of the projective line over the integers Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2608.15057 (math) [Submitted on 15 Aug 2026] Title: On branched coverings of the projective line over the integers Authors: Ryoji Shimizu , Naganori Yamaguchi View a PDF of the paper titled On branched coverings of the projective line over the integers, by Ryoji Shimizu and 1 other authors View PDF HTML (experimental) Abstract: We investigate the étale fundamental group of the complement of a horizontal divisor on $\mathbb{P}^{1}_{\mathbb{Z}}$. We prove that this group has no nontrivial finite solvable quotient if and only if the divisor is normal crossings at the prime~$2$. Moreover, if the divisor is normal crossings at the prime~$2$ and either has three irreducible components or is normal crossings at the prime~$3$, we show that no quotient isomorphic to $\mathrm{PSL}_{2}(q)$ can occur for certain prime powers~$q$. Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:2608.15057 [math.AG] (or arXiv:2608.15057v1 [math.AG] for this version) https://doi.org/10.48550/arXiv.2608.15057 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Naganori Yamaguchi [ view email ] [v1] Sat, 15 Aug 2026 06:09:50 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled On branched coverings of the projective line over the integers, by Ryoji Shimizu and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• On branched coverings of the projective line over the integers#611010
• Density of Vanishing of Certain Eigenspaces of Cyclotomic Class Groups#1083424
• Critical points of point charge potentials along lines#819790
• Critical points of point charge potentials along lines#809794
• A 6-functor formalism for solid quasi-coherent sheaves on the Fargues-Fontaine curve#986769