Math 203B - Algebraic Geometry (Winter 2016)

Course description: This course provides an introduction to algebraic geometry. Algebraic geometry is a central subject in modern mathematics, and an active area of research. It has connections with number theory, differential geometry, symplectic geometry, mathematical physics, string theory, representation theory, combinatorics and others.

Math 203 is a three-quarter sequence. Math 203A covered affine and projective varieties. Math 203B will focus more heavily on sheaves, schemes, and the modern language of algebraic geometry. Topics to be covered: sheaves and schemes; quasicoherent sheaves; sheaf cohomology; Riemann-Roch theorem for curves and applications; properties of morphisms of schemes (separated, proper, smooth, etale). Additional topics will be covered in Math 203C. (For some idea of my plans, see my past course web sites.)

Instructor: Kiran Kedlaya, kedlaya [at] math [etcetera], APM 7202.

Lectures: MWF 10-11, APM B412. Some lectures will be rescheduled to Tue 10-11, APM 5829; see the lecture calendar.

Office hours: To be announced week by week. Appointments can also be made by email.

Textbook: No required text. I will provide my own notes. It may be helpful to have access to a copy of Hartshorne, Algebraic Geometry but UCSD students can get it as a legal free e-book download using SpringerLink. You may also find helpful Ravi Vakil's Math 216 lecture notes. Initially the notes by Gathmann used in Math 203A may be helpful, but I will diverge from them fairly early on.

The ultimate technical reference for the theory of schemes is Grothendieck's EGA Johan de Jong's Stacks Project. Do not try to read it cover to cover! Instead, feel free to search through it for individual topics (including homework problems).

Prerequisites: Math 203A, preferably taken last quarter. If you do not meet this prerequisite, please contact me as soon as possible!

Grading: 100% homework (no final exam). Problem sets will be assigned weekly (see below); please do them! It is effectively impossible to learn this subject passively. Some flexibility with due dates is available as long as you ask before the original deadline. Collaboration and outside research is permitted; just declare it in as much detail as possible.


Homework: Problem sets may be submitted until 5pm on the due date in my department mailbox, or if you type your solutions you may submit via SageMathCloud. To set this up, create an account on SMC (a free account will suffice), then email me your username.

Calendar of lecture topics: