The structure sheaf of the moduli of oriented $p$-divisible groups

Research paper by Jack Morgan Davies

Indexed on: 02 Jul '20Published on: 01 Jul '20Published in: arXiv - Mathematics - Algebraic Topology

Abstract

Using spectral algebraic geometry, we define a derived moduli stack of oriented $p$-divisible groups and study its structure sheaf. This stack is consequently used to prove a theorem of Lurie which predicts the existence of a certain sheaf of $\mathbf{E}_\infty$-rings $\mathcal{O}^\mathrm{top}_{\mathrm{BT}_n^p}$ on a formally \'{e}tale site of the classical moduli stack of $p$-divisible groups. A variety of sections of this sheaf are then shown to be equivalent to known $\mathbf{E}_\infty$-rings in stable homotopy theory, and the natural symmetries on these sections also recover well-studied actions and operations.