  The Jacobian Conjecture uses the equation $det(Jac(F))\in k^*$, which is a
very short way to write down many equations putting restrictions on the
coefficients of a polynomial map $F$. In characteristic $p$ these equations do
not suffice to (conjecturally) force a polynomial map to be invertible. In this
article, we describe how to construct the conjecturally sufficient equations in
characteristic $p$ forcing a polynomial map to be invertible. This provides an
(alternative to Adjamagbo's formulation) definition of the Jacobian Conjecture
in characteristic $p$. We strengthen this formulation by investigating some
special cases and by linking it to the regular Jacobian Conjecture in
characteristic zero.
