In the last two posts, we made some basic constructions with finite group schemes (which are always assumed flat and commutative), and discussed their decompositions into connected, étale, multiplicative, and unipotent parts. Today we’ll bootstrap those constructions up to our real objects of interest: -divisible groups.

Here’s what I’ve been up to. The moduli stacks of -divisible groups chatter at my mind like winged monkeys, and so this series of posts is going to continue, slowly, into the indefinite future. I’m particularly interested in various ways of describing -divisible groups, so you should expect to hear from me about the Dieudonné correspondence, Dieudonné crystals, and possibly even Thomas Zink’s theory of ‘nilpotent displays.’ There’ll be a few asides on Witt vectors as well.

We’ve been doing a summer seminar on Goodwillie calculus at Northwestern, and I recently gave a talk about Nick Kuhn’s cool theorem that Goodwillie towers in spectra split after finite -localization. I’m in the process of making some fairly detailed notes about this paper, which should appear here shortly. I’m also going to a summer school in Oregon on infinity-categories, and will probably end up posting some notes on Thom spectra or whatnot as a result. Continue reading