Siegel's theorem on integral points and the Jacobian conjecture over the rational field

2015/02/01 by Nguyen Van Chau, Nguyễn Văn Vĩnh Châu, Van Chau, Nguyen
Mathematics · Physics and Astronomy · #11G05 #14R15 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.AG #msc:11G05 #msc:14R15

paper · pdf · doi:10.48550/arxiv.1502.00328

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openalex publication_date 2015/02/01 · arxiv created 2016/10/17 · arxiv updated 2016/10/18 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

It is shown that a polynomial map (P,Q)∈ ℚ[x,y]² with P_xQ_y-P_yQ_x ≡ 1 has an inverse map in ℚ[x,y]² if the fiber P=0 contains an infinite subset of d^-1ℤ² for an integer d.

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