Lubin-Tate Theory

Motivation: We seek to understand the stable homotopy category by understanding the structure of the moduli stack of formal groups. Over algebraically closed fields, this is straightforward. If char(k) = 0, every formal group law is isomorphic to the additive one and we’ve described the group of automorphisms (coordinates changes) before. If char(k) = p > 0 every formal group law is classified by its height. Furthermore, the automorphism group of a height n formal group law over k is the Morava stabilizer group Sn, which can be described as the units in a certain division algebra. For fields of characteristic p that are not algebraically closed, we can do Galois descent (a good topic for a future talk). The next case to consider is a complete local Noetherian ring with residue field k of characteristic p > 0. Goal: Describe formal group laws over complete local Noetherian rings and their automorphisms.