Math 221, Commutative Algebra

Instructor: Mihnea Popa

Mihnea Popa
Office: SC 537
Tel: 617-495-4825
email: mpopa@math.harvard.edu
  • Meeting times: WF 10:30-11:45 via Zoom
  • First meeting: Friday, September 4, 2020
  • Office hours: Thursday 1.30-2.30pm, and by appointment
  • CAs:     Christopher Dowd cjdowd@college.harvard.edu     and Mikayel Mkrtchyan mkrtchyan@college.harvard.edu
  • Recommended books: During the first part of the course we will often use M. Atiyah and I. G. MacDonald, "Introduction to Commutative Algebra"; during the second part, we will sometimes make use of D. Eisenbud, "Commutative Algebra with a view toward Algebraic Geometry", and H. Matsumura, "Commutative Ring Theory". I will also use personal lecture notes throughout the course.
Brief course description: Primary decomposition and associated primes. Integral extensions, going up and going down theorems. Noether normalization. Dimension theory. Depth, regular sequences, Cohen-Macaulay rings. Homological methods. Regular local rings. Auslander-Buchsbaum theorem.
Recommended Prep: Math 122-123 (Algebra I-II)
Technical details: The course will consist of Zoom delivered regular lectures. Zoom and other technical details will appear on the Canvas course page. This page will be updated regularly.
Requirements: Everyone is expected to attend class on a regular basis, with the camera on (barring special circumstances). There will be weekly homework, posted on Canvas and on this page every Wednesday, and due the following Wednesday. Homework is the most important component of this course, counting for 80% of your grade. Normally no late homework will be accepted, but the lowest score will be dropped. You are encouraged to collaborate on the homework problems, but you must write your own solutions and properly acknowledge any collaboration, or help you receive from others. There will also be a small written final project on a topic of interest, on which you will work in teams. Together with class participation, this will account for 20% of the final grade. There is no final.
Homework :