Awhile ago I was talking mainly about algebra. I was mostly going by what I was reading in Matsumura, but recently the chapters in Matsumura that I’ve been reading I’ve already covered in previous posts, so I didn’t want to reopen those topics. This has been one of the main causes of my hiatus. My guess is that in general this quarter will be a lot sparser in posts.
Two ideas of where to go while I wait for my algebra to get back to a point where I can start posting again is to start in on some of the basic constructions underlying modern algebraic geometry, like developing sheaves and schemes. This seems to have been covered in a few other blogs, so I’m hesitant.
The other thing that would be really neat, and I’m pretty sure has not been covered by any other blog is to talk about spectral sequences. Right now I’m in a homological algebra class that is essentially devoted to them. I think they are quite a fascinating and brilliant construction. The main thing I’d like to do on this blog is to see where they come up in algebraic geometry, since this particular application is sure to not come up in class.
The problem with this is that it would be an incredibly massive undertaking. Just motivating and explaining the construction would take a long time. I would also really need to figure out a good way of doing diagrams in wordpress.
In any case, just thought I’d check in and see if anyone had opinions one way or another.