algebraic geometry 30 The Ax Grothendieck theorem
Channel: Richard E Borcherds
Date: 2020-06-06

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the Ax-Grothendieck theorem, which states that an injective regular map between varieties is surjective. The proof uses a strange technique: first prove the result in characteristic greater than 0, then prove it in characteristic 0 using the fact that the first order theory of algebraically closed fields of characteristic 0 is complete.