Schemes 30: f* and f *
Channel: Richard E Borcherds
Date: 2020-07-23

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.
Given a morphism of schemes, we define two maps f^* and f_* 
taking  sheaves of modules on one space to sheaves of modules on the other, and discuss their exactness properties. We also briefly discuss the operation of extension by 0.

Warning: at one point in this video I originally implied that f_* takes quasicoherent sheaves to quasicoherent sheaves, which is usually but not always true. I have tried to edit out this error, 
but it is possible I missed somewhere where this mistake occurs.