Commutative Algebra Autumn 2019

Exercise classes

G-01 Thu 9-10, HG F 26.5

G-02 Thu 12-13, HG E 33.1

Starting dates

First lecture: Wed, September 18, 2019

First exercise class: Thu, September 19, 2019

Content

This course provides an introduction to commutative algebra as a foundation for and first steps towards algebraic geometry. We shall cover approximately the material from most of the textbook by Antoine Chambert-Loir and by Atiyah-MacDonald.

Topics include:

• Basics about rings, ideals and modules
• Localization
• Primary decomposition
• Integral dependence and valuations
• Noetherian rings
• Completions
• Basic dimension theory

Prerequisites

Algebra I (or a similar introduction to the basic concepts of ring theory).

Exercises

The new exercises will be posted here on Friday afternoon (or Monday morning). We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Thursday.

Please hand in your solutions by the following Friday at 12:00 in room HG J68, in the box under the sign corresponding to the course. Please do not forget to write the name of your teaching assistant on each sheet that you hand in. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68. Written solutions will be provided the day after the deadline for handing them in.

Exercise classes

Examination Rules

Literature

1. "(Mostly) Commutative Algebra" by Antoine Chambert-Loir

2. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969)

4. "Algebraic Geometry and Commutative Algebra" by S. Bosch (Springer 2013)
5. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989)
6. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995)
7. "Commutative Algebra" by N. Bourbaki (Hermann, Masson, Springer)