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 and the basics of scheme theory. Math 203B will focus more heavily on the theory of schemes and the modern language of algebraic geometry. Topics to be covered: review of sheaves and schemes; quasicoherent sheaves; sheaf cohomology; Riemann-Roch theorem for curves and applications; properties of morphisms of schemes (separated, proper, smooth, etale). See also the Math 203C home page.
Instructor: Kiran Kedlaya, kedlaya [at] math [etcetera], APM 7402.
Lectures: MWF 12-1, APM 7421. (Makeup lectures may be scheduled differently.)
Office hours: TBA. Appointments can also be made by email.
Textbook: No required text. We will start where Math 203A left off in Andreas Gathmann's notes, but later I will diverge from these notes and start supplying my own notes.
It may be helpful to have access to a copy of Hartshorne, Algebraic Geometry; it has been placed on reserve at Geisel Library.
The ultimate technical reference for the theory of schemes is
Grothendieck's EGA Johan de Jong's Stacks Project.
Prerequisites: Math 203A, preferably taken last quarter. If you do not meet this prerequisite, please contact me as soon as possible!
Grading: 100% homework. Problem sets will be assigned weekly (see below); please do them! It is effectively impossible to learn this subject passively. (If you are a graduate student, I will only grade your homework if you are registered for the course. Please register!)