The previous lecture in this series is here. The next lecture in this series is here.
This lecture 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.
This video is part of a lecture course by Richard Borcherds from 2020.