Professor A.J. de Jong, Columbia university, Department of Mathematics.
This semester I am teaching the course on schemes. If you are interested, please email me, tell me a little about yourself (academically), and I will add you to my email list.
The first lecture will be Wed, Jan 22 at 4:10pm - 5:25pm in 507 Math. The schedule will be Monday and Wednesday at 4:10 in 507 Math.
To keep up with the course it is **very important** to both attend the lectures and to work on the problem sets. I know that my problem sets are often impossible and grading will reflect this. Please focus on doing some of the problem set each week and do not try to do all of the problems completely.
There is no TA. I will have office hours starting at 3:00 pm on Thursday in my office and continuing through tea (I will be in the common room during tea time).
Exam. Thu, May 12 2025 at 4:10-7:00pm in MATH 507
Content. The goal is to esthablish the existence of the Picard variety or Jacobian of a (projective, smooth) curve and to deduce some properties of the Picard group of a curve from this (using a tiny bit of the geometry of abelian varieties). This is too much to cover in a 1 semester course, so we will have to blackbox lots of material. Still, I think we can carefully work through the key arguments of the proof.
Readings. We will use the exposition in the Stacks project, especially the chapter on Picard Schemes of Curves and the section on Abelian varieties.
Here is a preliminary list of things I intend to discuss:
Problem sets. Hand the solutions to me personally, or slide them under my door in the building, or email them to me. Some of the exercises will be impossible, so it should not be your goal to do each and every one of them. Moreover, these exercises are not always doable purely with the material discussed in the course -- sometimes you'll have to look up things online or in books and use what you find.
PS: To find the webpages for previous semesters, please visit this page