Last year I participated in the MaBloWriMo project of blogging every day for a month about a topic. I think I learned a bit of differential geometry as a result, and it was fun. But this semester, I have not really blogged very much. It’s partially been business and partially laziness. Given all the homework write-ups for my classes, the urge to blog is just subdued.

So my announcement that I am going to do MaBloWriMo again probably sounds rather silly. Nonetheless, I would like to give it a shot. I will probably not be able to post every day, but I’ll see if I can get at least fifteen posts up next month.

The plan is as follows. I will talk about commutative algebra, specifically the homological theory. Here are some of the topics I’d like to touch on:

  • Basic properties of depth and the analogy to codimension
  • The Auslander-Buchsbaum formula relating depth and projective dimension
  • Cohen-Macaulay rings and their basic properties
  • Properties of regular local rings (in particular, factoriality and the characterization in terms of finite global dimension)
  • Koszul homology and cohomology, and the application to the quasi-coherent cohomology of an affine scheme (as in EGA III)
  • How this all figures in Serre duality

That I think should be enough for several posts! Unlike last time, I will assume prior acquaintance with commutative algebra for these posts, in particular at the level of dimension theory.  We’ll see how well I keep my promises.

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