Schemes 37: Comparison of Weil and Cartier divisors
Channel: Richard E Borcherds
Date: 2020-07-29

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne.
In this lecture we compare Cartier and Weil divisors, showing that for Noethernian integral schems the map from Cartier to Weil divisors is injective if the scheme is normal ind an isomorphism if the scheme is locally factorial. We also give some examples where the the map is not injective or not surjective.