Algebraic geometry II - schemes and sheaves

In this lecture, we covered the following topics:

-corrected the setup for Weil divisors, to include the assumption that the scheme is regular in codimension 1;

-definition of sheaf associated to a Weil divisor;

-motivation for Cartier divisor stemming from transition functions of vector bundles on manifolds;

-definition of Cartier divisor and local representability by the class of a rational function;

-homomorphism from Cartier divisors to Weil divisors and conditions for it to be injective;

-Cartier divisors correspond to locally principal Cartier divisors;

-example of a line through the vertex in the round cone;

-Weil divisors coincide with Cartier divisors if the underlying scheme is locally factorial (no proof).