## AGCA: HBT Proof and a sweet Bijection.

### August 27, 2010

It’s becoming a bit more difficult to write these, with grading and homework taking up much of my time, and I no longer am officially "taking" AGCA for credit. Nonetheless, it’s an extremely interesting topic, and I’m going to go along with it for as long as I can. I should have noted in the previous post: a ring will always mean "commutative, with unit."

Okay, first, I’m going to abbreviate Algebraic Geometry + Commutative Algebra as AGCA, since, you know, it’s a lot to say. Second, these posts (with the title AGCA) may require a bit more mathematical maturity and abstract algebra than the others.

This is following the lectures of Professor Vitter, and, unfortunately, is only going to be a shallow copy with, most likely, more typos. My intention is to learn the material by teaching, and to clear up and expand on the proofs given. I do not pretend to be anywhere near as good a lecturer or mathematician, and this post is essentially “for entertainment purposes only.” Reader beware.