2025/09/23 by Yuan, Yijun
#03B35 #14G40 #14H60 #68V15 #68V20 #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2509.19632
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