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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.19632 |
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Table of 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