**R.V. Gurjar**

IIT, Mumbai

October 12, 2017

**Generalized Jacobian Conjecture**:
M. Miyanishi generalized the usual Jacobian Conjecture as follows.
Generalized Jacobian Conjecture. Let V be a normal affine variety. Suppose f:V o V is an unramified morphism. Then f is a proper morphism.
After discussing some earlier positive results and some counterexamples to GJC we will outline the proof of the following result proved jointly with M. Miyanishi.
Theorem. Let V be an irreducible normal affine surface. Assume that V has at least one singular point which is not a quotient singular point. Then any unramified self morphism is an isomorphism.