This talk will introduce a new machine: approximable triangulated categories. The applications so far are: (1) Proofs of conjectures of Bondal, Van den Bergh and Rouquier about strong generation, and (2) A really short, one-page proof of Serre’s old GAGA theorem.
In my ARC application I made the case that, given the successes so far, this machine is worth developing further.
As you may know the ARC decided to give me lots of money last year, even though I’m not exactly either a healthy man or a young man. The grant proposal, which a few of you saw, made the case that the mathematics I have done in the last five years is exceptional enough so that an old fogey like me should be allowed to recruit young people to continue the work, once I’m no longer able to.
My plan is to give a series of talks, to those of you who might be interested in joining me on this project. Presumably the audience will be small, no more than half a dozen. But the first talk is intended to be broad and introductory and will assume little background.