Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

2024/01/20 by Hao Chang, Chang, Hao, Bin Shu +3
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Control and Dynamics of Mobile Robots #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2401.11072

openalex publication_date 2024/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism φ of the polynomial ring k[x₁,…,x_n], if φ preserves the maximal ideals, then φ is an automorphism.

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