Formalization of Harder-Narasimhan theory

Yijun Yuan

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arXiv · 2509.19632

Formalization of Harder-Narasimhan theory

Yijun Yuan

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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-H\"older filtration for a semistable Harder-Narasimhan game.

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Yijun Yuan. 2025-09-23. Formalization of Harder-Narasimhan theory. https://arxiv.org/abs/2509.19632

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