2005/07/26 by Richard J. Lipton, Evangelos Markakis, Lipton, Richard J. +1
Mathematics · Physics and Astronomy · #14R15 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:14R15
paper · pdf · doi:10.48550/arxiv.math/0507525
12 pages
arxiv created 2005/07/26 · openalex publication_date 2005/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We make two observations regarding the invertibility of Keller maps. i.e., polynomial maps for which the determinant of their Jacobian matrix is identically equal to 1. In our first result, we show that if P is a n-dimensional Keller map, defined over any extension of Q, then P has a polynomial inverse if and only if the range of P contains the cartesian product of n universal Hilbert sets. In our second result, we show that if P is a 2-dimensional Keller map, defined over any algebraic number field, then P is invertible on a set that contains almost all rational integers of K.