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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2509.19632 |
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| _version_ | 1866918339114172416 |
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| author | Yuan, Yijun |
| author_facet | Yuan, Yijun |
| contents | 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 the formalization of Harder-Narasimhan theory in the proof assistant Lean 4 with Mathlib. This formalization is based on a recent approach of 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 coprimary filtration of a finitely generated module over a noetherian ring, and the existence of the Jordan-Hölder filtration of a semistable Harder-Narasimhan game.
Code available at: https://github.com/YijunYuan/HarderNarasimhan |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formalization of Harder-Narasimhan theory Yuan, Yijun Algebraic Geometry Formal Languages and Automata Theory Logic in Computer Science Number Theory 68V20, 14H60, 03B35, 06B23, 91A80 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 the formalization of Harder-Narasimhan theory in the proof assistant Lean 4 with Mathlib. This formalization is based on a recent approach of 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 coprimary filtration of a finitely generated module over a noetherian ring, and the existence of the Jordan-Hölder filtration of a semistable Harder-Narasimhan game. Code available at: https://github.com/YijunYuan/HarderNarasimhan |
| title | Formalization of Harder-Narasimhan theory |
| topic | Algebraic Geometry Formal Languages and Automata Theory Logic in Computer Science Number Theory 68V20, 14H60, 03B35, 06B23, 91A80 |
| url | https://arxiv.org/abs/2509.19632 |