Contents:
We will cover the first three chapters of Hartshorne’s book “Algebraic Geometry”. This is a “must” to students who plan to study arithmetic geometry.
Specifically, we will discuss some aspects of classical algebraic geometry to illustrate the motivation of sheaf theory and scheme theory. Then we will move to scheme theory and its cohomology theory.

Course prerequisite:
A course of algebra for graduate students.

Reference material (textbook(s))
Hartshorne, Algebraic Geometry, GTM.vol.52, Springer-Verlag 1977
Shafarevich, Basic algebraic geometry, Second edition, Springer-Verlag, 1994.

Grading scheme:
20%, attention;
80%, final examination.

Course Goal:
An introduction to scheme theory and sheaf cohomology. The students may study the parts of Hartshorne’s book after this year to get a whole picture of algebraic geometry.