Variations on a theme of Faltings

The complex unit disc is conformally equivalent to the upper half-plane. In 2002, Faltings proved a p-adic version: the p-adic unit disc is isomorphic to Drinfeld’s upper half-plane, up to the action of some profinite groups. We report on some work in progress concerning a family of Faltings-style isomorphisms, occurring entirely in characteristic p. These concern moduli spaces of formal groups over a local base where the generic and special fibers have specified heights. We were motivated to study these spaces by problems in chromatic homotopy theory. This is joint work with many people.

Pretalk abstract: The pre-talk will give more details about the original Faltings isomorphism.