Not offered in 2017/2018

Dima Arinkin: Spring 2016

This course is the continuation of Math 763. The goal is to put to extend the framework of algebraic geometry from varieties (studied in Math 763) to schemes. This requires using the language of sheaves (and, particularly, sheaves of rings) on topological spaces.

In the beginning of the course, we will go over basic properties of sheaves. We will then define schemes and morphisms of schemes, and study various classes of morphisms. Time permitting, I hope to discuss (quasi)coherent sheaves on schemes.

Standard references on this subject include:

- Hartshorne,
*Algebraic Geometry* - Shafarevich,
*Basic Algebraic Geometry* - Ravi Vakilâ€™s notes,
*The Rising Sea*