[2310.01289] Chai's conjectures on base change conductors Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2310.01289 (math) [Submitted on 2 Oct 2023 ( v1 ), last revised 16 Jun 2025 (this version, v3)] Title: Chai's conjectures on base change conductors Authors: Otto Overkamp , Takashi Suzuki View a PDF of the paper titled Chai's conjectures on base change conductors, by Otto Overkamp and 1 other authors View PDF HTML (experimental) Abstract: The base change conductor is an invariant introduced by Chai which measures the failure of a semiabelian variety to have semiabelian reduction. We investigate the behaviour of this invariant in short exact sequences, as well as under duality and isogeny. Our results imply Chai's conjecture on the additivity of the base change conductor in short exact sequences, while also showing that a proposed generalisation of this conjecture fails. We use similar methods to show that the base change conductor is invariant under duality of Abelian varieties in equal positive characteristic (answering a question of Chai), as well as giving a new short proof of a formula due to Chai, Yu, and de Shalit which expresses the base change conductor of a torus in terms of its (rational) cocharacter module. Comments: Accepted for publication in Journal of Algebraic Geometry. 44 pages Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) MSC classes: 14K15 (Primary), 14G20, 11G45, 14F20, 11G10 (Secondary) Cite as: arXiv:2310.01289 [math.NT] (or arXiv:2310.01289v3 [math.NT] for this version) https://doi.org/10.48550/arXiv.2310.01289 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Algebraic Geom. 35 (2026), no. 3, 523-569 Related DOI : https://doi.org/10.1090/jag/855 Focus to learn more DOI(s) linking to related resources Submission history From: Takashi Suzuki [ view email ] [v1] Mon, 2 Oct 2023 15:42:15 UTC (37 KB) [v2] Sun, 4 May 2025 02:17:43 UTC (35 KB) [v3] Mon, 16 Jun 2025 07:44:53 UTC (36 KB) Full-text links: Access Paper: View a PDF of the paper titled Chai's conjectures on base change conductors, by Otto Overkamp and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2023-10 Change to browse by: math math.AG 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