Math 203B - Algebraic Geometry (Winter 2020)

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 3-3:50, APM B412. A few lectures will be cancelled and made up at other times (to be agreed upon); see the lecture calendar.

Office hours: Mon 4-5. Appointments can also be made by email.

Textbook: Hartshorne, Algebraic Geometry. UCSD students can get it as a legal free PDF download using SpringerLink. You may also find helpful Ravi Vakil's Math 216 lecture notes. I will occasionally post lecture notes on specific topics.

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, but please ask before the original deadline. Collaboration and outside research is permitted and encouraged; just declare it in as much detail as possible.


Problem sets may be submitted until 6pm on the due date in my department mailbox. Typed solutions may also be submitted as email (please send a PDF file).

Calendar of lecture topics: