Math
629 002: Commutative Algebra II (Fall, 2013)

Here's a syllabus (which may be amended in the near future).

Here's homework assignment 1.

Some resources to use before we get to Bruns & Herzog:

- On flatness, exact sequences, etc.: See just about any textbook on homological algebra -- Rotman, Weibel, etc.
- On Krull's height theorem and principal ideal theorem: I used
section 3.2 of Kaplansky's book.

- On completion: see Hochster's notes, chapter 4 of Ash's online textbook, or chapter 7 of Eisenbud's 1995 volume. See also Dan Katz's notes on Hensel's lemma.
- On the Cohen structure theorem: see Hochster's notes on this, Eisenbud chapter 7 again, or Dan Katz's "Guide".

Here's homework assignment 2. (Of course, all theorem numbers and such are references to Bruns and Herzog.)

Here's homework assignment 3.

Regarding the Koszul complex: We won't need to explore it in the kind of depth that the book contains. Hence, my source material on the Koszul complex will come largely from Matsumura (pp. 127-131) with some help from Hochster's notes. (Note there are two links, to consecutive lectures. They also contain information we don't need. Start the first link on p.5, under the heading "Mapping Cones".)

For further understanding of the Koszul complex, check this out if you like.

Here's homework assignment 4.

For a limited time only, some hints and answers to assignments 2 and 3!

And now, solutions to assignment 4 as well.