Professor A.J. de Jong, Columbia university, Department of Mathematics.

I'd like to create a mailing list for people interested in this course so please email me if you are interested in attending the lectures (even if you aren't going to attend all the lectures, etc).

The plan of this semester course in commutative algebra is to focus on interesting nontrivial results rather than building theory from the ground up. You will have to work to be able to keep up with the material including reading up on background material and doing exercises that explain the basics.

More specifically, I hope to cover a lot of basic dimension theory of Noetherian rings (especially rings of finite type over a field), and I hope to explain the algebraic version of Zariski's Main Theorem as well as applications (especially to dimension theory).

There is not going to be a book associated to the course. All of the material will be in some form or other in the chapter on commutative algebra of the stacks project.

It is ** strongly** encouraged to go to the lectures, which are on
Monday and Wednesday 11:00-12:15 in Math 307.

Problem sets will be announced in lecture on wednesdays and on this web page. They are due in lecture on the next Wednesday. Please write out all arguments completely.

The TA for the course is Jie Xia.

Grades are computed by a weighted average between the scores on problem sets and final. The weights are 2/3 and 1/3 respectively.

The final will be a written exam.

Here are the weekly problem sets. Please hit the refresh button on your browser to make sure you have to latest list. These exercises are partially meant for you to see if you know enough to be able to follow the material in the course. Hence it is suggested that you skip the ones you are familiar with, or give a very brief answer showing you understand the point. Moreover, most of the exercises are of a theoretical nature, hence you'll be able to look up that answer -- feel free to do this.

- From Exercises do Exercise 5.1, 5.2, 5.3, 5.5, 5.10, 5.29.
- From Exercises do Exercise 5.30, 6.1, 6.2, 6.3, 6.4, 6.5 (these are about localization -- make sure you download the latest version of the exercises chapter).
- From Exercises do Exercise 7.1, 8.2, 8.3, 8.4, 11.1, 11.2.
- From Exercises do Exercise 10.1, 10.3, 10.5, 13.1.
- From Exercises do Exercise 11.3, 12.3, 14.1, 17.2, 17.3.
- From Exercises do Exercise 9.1, 19.6 (difficult -- see if you can solve the easier 19.4 and 19.5 before attempting this one), 19.8, 21.4, 21.5.
- From Exercises do Exercise 1.9, 1.10, 16.1 part (1), 20.4 (warning: parts (6) and (7) are not completely straightforward).
- From Exercises do Exercise 1.4, 2.2, 2.4, 2.5, 2.6, 22.1. (I recall that you are allowed to quote things you have seen in books you have read, etc.)
- First read a little bit about tensor products; enough to do the first of these exercises. From Exercises do Exercises 15.2, 15.4, and 15.5.
- From Exercises do Exercises 24.1, 25.1, 25.9, and 25.10. Please take a look at the statements of exercises 25.2 and 25.3 also, since they will be frequently used in the lectures in the future.
- From Exercises do Exercises 26.1, 26.2, 26.4, 26.7, 26.10, and 26.11.
- (Due Monday, December 12.) From Exercises do Exercises 26.14, 26.16, 27.3, and 27.5.