The Jacobian Conjecture

In this chapter, we address the most famous of the problems about polynomial mappings: Problem 5.0.1 (the Jacobian conjecture). If for n polynomials p1, ... , p n ∈ K[x1, ... , x n ], the corresponding Jacobian matrix is invertible, then K[p1, ... , p n ] = K[x1, ... , x n ].