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Lecturer: Owen Biesel bieselod@math.leidenuniv.nl (no longer valid; use the Contact form)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):
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- 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
- March 10: Resit Exam
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.
Owen Biesel 