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.

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My understanding is that bloggers who need commutative diagrams embed them as images.

Just something to think about, at least in the corner of algebraic geometry where I’m reading papers right now, the words “spectral sequence” seem to have gone out of style, and people are using the machinery of hypercohomology when writing their papers. If you could talk about that and provide a dictionary between the two approaches, that’d be good (and, it’s something you might want to learn anyway).

My entirely selfish suggestion is spectral sequences because I’ve been trying to grok them for something like a year on and off without success. I have really no idea whether there is a way to do it in blog format though.

When I do commutative diagrams, I embed them as images.

“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.”

It would be especially useful — at least for the blogging community — to have someone make a nice (spectral) sequence of posts on spectral sequences. As I understand it many people have planned on studying this topic for some time, to evidently no avail. In any case, I have not seen any posts on them. Thus we bloggers acknowledge your coming pains, and nevertheless forcefully shove the collective torch into your hands…!