Schemes 10: Morphisms of affine schemes
Channel: Richard E Borcherds
Date: 2020-07-07

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.
We try to define  morphisms of schemes. The obvious definition as morphisms of ringed spaces fails as we show in an example. Instead we have to use the more subtle concept of a morphism of locally ringed spaces. This can then be used to show that morphisms of rings correspond exactly to morphisms of affine schemes. We conclude by using this to show that the plane minus the origin is not an affine scheme.