Characteristic p approaches to the Jacobian conjecture

Abstract

We present several versions of the Jacobian Conjecture in characteristic $p>0$ each of which if true would imply the Jacobian Conjecture in characteristic 0. We test these characteristic p versions of the conjecture against several families of Jacobian pairs in characteristic p. Based on the results we propose a characteristic p approach to solving the Jacobian Conjecture in characteristic 0.