A p-adic approach to the Jacobian Conjecture

It is shown that the Jacobian Conjecture (in all dimensions) is equivalent to the following statement: for almost all prime numbers p   and each Keller map F∈Zp[X]nF∈Zp[X]n (i.e. det⁡JF=1det⁡JF=1), the induced map F¯:Fpn→Fpn is not the zero map.