Formalization of Harder-Narasimhan theory

[2509.19632] Formalization of Harder-Narasimhan theory Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2509.19632 (math) [Submitted on 23 Sep 2025 ( v1 ), last revised 24 Sep 2026 (this version, v5)] Title: Formalization of Harder-Narasimhan theory Authors: Yijun Yuan View PDF HTML (experimental) Abstract: The Harder-Narasimhan theory provides a canonical filtration of a vector bundle on a projective curve whose successive quotients are semistable with strictly decreasing slopes. In this article, we present a formalization of Harder-Narasimhan theory in the proof assistant Lean 4 with Mathlib. The formalization is based on a recent approach to Harder-Narasimhan theory by Chen and Jeannin, which reinterprets the theory in order-theoretic terms and avoids the classical dependence on algebraic geometry. As an application, we formalize the uniqueness of the coprimary filtration of a nontrivial finitely generated module over a Noetherian ring, as well as the existence of a Jordan-Hölder filtration for a semistable Harder-Narasimhan game. Comments: 28 pages Subjects: Algebraic Geometry (math.AG) ; Formal Languages and Automata Theory (cs.FL); Logic in Computer Science (cs.LO); Number Theory (math.NT) MSC classes: 68V20, 14H60, 03B35, 06B23, 91A80 Cite as: arXiv:2509.19632 [math.AG] (or arXiv:2509.19632v5 [math.AG] for this version) https://doi.org/10.48550/arXiv.2509.19632 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yijun Yuan [ view email ] [v1] Tue, 23 Sep 2025 22:45:49 UTC (713 KB) [v2] Sun, 4 Jan 2026 06:54:12 UTC (464 KB) [v3] Sun, 15 Feb 2026 04:29:40 UTC (487 KB) [v4] Thu, 27 Aug 2026 09:07:11 UTC (57 KB) [v5] Thu, 24 Sep 2026 15:13:13 UTC (62 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2025-09 Change to browse by: cs cs.FL cs.LO math math.NT References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation 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 (opens in new tab) (opens in new tab) (opens in new tab)

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