Here are the course materials for Commutative Algebra, taught at Leiden University in Fall 2015.

**Lecturer:** Owen Biesel bieselod@math.leidenuniv.nl (no longer valid; use the Contact form)

**Grader:** Erik Visse h.d.visse@math.leidenuniv.nl

**Time and Place:** 11:15-13:00 on Mondays in Snellius room 401.

**Office Hours:** Make an appointment or drop by whenever you see me in my office (233); if this gets out of hand I will make an official office hour.

**Recommended Reading:** I find David Eisenbud’s “Commutative Algebra with a View Toward Algebraic Geometry” to be a readable and comprehensive reference, but you do not need a copy to follow this course.

**Grades spreadsheet:** A view-only and anonymized grades spreadsheet is now visible here.

### Course Outline (so far):

**August 31:**Noetherian rings and modules. Homework 1 (tex)**September 7:**Hom and Tensor. Homework 2 (tex)**September 14:**Localization. Homework 3 (tex)**September 21:**Supports of modules. Homework 4 (tex)**September 28: No class.****October 5:**Associated primes. Homework 5 (tex)**October 12:**Primary Decomposition. Homework 6 (tex)**October 19:**Integrality and the Nullstellensatz. Homework 7 (tex)**October 26:**Flat Modules and Algebras. Homework 8 (tex)**November 2: No class.****November 9:**Dimension (Zero) and Length. Homework 9 (tex)**November 16:**Going Up and Down. Homework 10 (tex)**November 23:**Completions and Blowups. Homework 11 (tex)**November 30:**Associated Graded Rings. Homework 12 (tex)**December 7:**The Fundamental Theorem of Dimension Theory. No homework!**January 13:**Final Exam, with solutions and comments.**March 10:**Resit Exam, with solutions and comments.

### Announcements (in reverse chronological order):

October 26: Writing Advice

- Erik has written up some general instructions for writing problem set solutions on his website. He may refer to these instructions while marking the homework.

August 28: Grading

**60%: Homework.**Each assignment is posted on Tuesday and due by email to Erik by the beginning of the next class (11:15am on Monday). The lowest two of the twelve homework scores are dropped.**40%: Written Final Exam.**The exam is scheduled for 2:00-5:00 on Wednesday, January 13 in room 174. The resit time is 10:00-1:00 on Thursday, March 10, also in room 174.