# Polynomials

## Jacobian Conjecture ★★★

Author(s): Keller

\begin{conjecture} Let $k$ be a field of characteristic zero. A collection $f_1,\ldots,f_n$ of polynomials in variables $x_1,\ldots,x_n$ defines an automorphism of $k^n$ if and only if the Jacobian matrix is a nonzero constant. \end{conjecture}

Keywords: Affine Geometry; Automorphisms; Polynomials