Injectivity of Keller Mappings

TL;DR

This paper proves that Keller mappings derived from Jacobi pairs are injective, thereby confirming the 2-dimensional Jacobi conjecture, which has been a longstanding open problem in mathematics.

Contribution

The paper establishes the injectivity of Keller mappings for Jacobi pairs, providing a proof of the 2-dimensional Jacobi conjecture.

Findings

Keller mappings from Jacobi pairs are injective

The 2-dimensional Jacobi conjecture is proven true

Injectivity holds for all Jacobi pairs in C[x,y]^2

Abstract

It is proved that for a Jacobi pair $(F,G)\in C[x,y]^2$, the Keller mapping: $(a,b)\mapsto(F(a,b),G(a,b))$ for $(a,b)\in C^2$, is injective. In particular, the $2$-dimensional Jacobi conjecture holds.