There are no Keller maps having prime degree field extensions

2024/07/16 by Vered Moskowicz, Moskowicz, Vered
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2407.13795

openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-dimensional Jacobian Conjecture says that a Keller map f: (x,y) ↦ (p,q) ∈ k[x,y]² having an invertible Jacobian is an automorphism of k[x,y]. We prove that there is no Keller map with [k(x,y): k(p,q)] prime.

Related

• Irreducibility properties of Keller maps
• Some Remarks on the Jacobian Conjecture and Connections with Hilbert's Irreducibility Theorem
• Frameworks for two-dimensional Keller maps
• Generalizations of local bijectivity of Keller maps and a proof of 2-dimensional Jacobian conjecture
• Injectivity of Keller Mappings