{"article_processing_charge":"No","type":"journal_article","doi":"10.2140/ant.2025.19.2049","publication":"Algebra & Number Theory","day":"05","author":[{"last_name":"Browning","first_name":"Timothy D","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","full_name":"Browning, Timothy D"},{"full_name":"Lyczak, Julian","first_name":"Julian","last_name":"Lyczak"},{"first_name":"Arne","last_name":"Smeets","full_name":"Smeets, Arne"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        19","publication_identifier":{"issn":["1937-0652"],"eissn":["1944-7833"]},"article_type":"original","publication_status":"published","date_updated":"2026-02-17T11:59:57Z","department":[{"_id":"TiBr"}],"volume":19,"date_created":"2026-02-16T15:22:19Z","external_id":{"arxiv":["2310.01135"]},"PlanS_conform":"1","oa_version":"Published Version","publisher":"Mathematical Sciences Publishers","corr_author":"1","has_accepted_license":"1","year":"2025","_id":"21244","ddc":["510"],"arxiv":1,"page":"2049-2090","project":[{"_id":"26AEDAB2-B435-11E9-9278-68D0E5697425","name":"New frontiers of the Manin conjecture","call_identifier":"FWF","grant_number":"P32428"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"citation":{"apa":"Browning, T. D., Lyczak, J., &#38; Smeets, A. (2025). Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>","ista":"Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations with multiple fibres. Algebra &#38; Number Theory. 19(10), 2049–2090.","ieee":"T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations with multiple fibres,” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10. Mathematical Sciences Publishers, pp. 2049–2090, 2025.","mla":"Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>, vol. 19, no. 10, Mathematical Sciences Publishers, 2025, pp. 2049–90, doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>.","ama":"Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with multiple fibres. <i>Algebra &#38; Number Theory</i>. 2025;19(10):2049-2090. doi:<a href=\"https://doi.org/10.2140/ant.2025.19.2049\">10.2140/ant.2025.19.2049</a>","short":"T.D. Browning, J. Lyczak, A. Smeets, Algebra &#38; Number Theory 19 (2025) 2049–2090.","chicago":"Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational Points on Fibrations with Multiple Fibres.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/ant.2025.19.2049\">https://doi.org/10.2140/ant.2025.19.2049</a>."},"issue":"10","file":[{"relation":"main_file","file_size":1505580,"checksum":"e50a60a4303b81563f7adbcadbe2e986","date_created":"2026-02-17T11:56:20Z","content_type":"application/pdf","date_updated":"2026-02-17T11:56:20Z","file_id":"21300","file_name":"2025_AlgebraNumberTheory_Browning.pdf","success":1,"access_level":"open_access","creator":"dernst"}],"abstract":[{"text":"Given a family of varieties over the projective line, we study the density of fibres that are everywhere locally soluble in the case that components of higher multiplicity are allowed. We use log geometry to formulate a new sparsity criterion for the existence of everywhere locally soluble fibres and formulate new conjectures that generalise previous work of Loughran and Smeets. These conjectures involve geometric invariants of the associated multiplicity orbifolds on the base of the fibration in the spirit of Campana. We give evidence for the conjectures by providing an assortment of bounds using Chebotarev’s theorem and sieve methods, with most of the evidence involving upper bounds. ","lang":"eng"}],"OA_type":"diamond","OA_place":"publisher","status":"public","file_date_updated":"2026-02-17T11:56:20Z","date_published":"2025-09-05T00:00:00Z","acknowledgement":"We are very grateful to Tim Santens for useful conversations and to the anonymous referees for numerous pertinent remarks. While working on this paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for Scientific Research – Flanders.","quality_controlled":"1","oa":1,"title":"Paucity of rational points on fibrations with multiple fibres","month":"09","language":[{"iso":"eng"}]}