The Devinatz-Hopkins Theorem via Algebraic Geometry

TL;DR

This paper demonstrates how the Devinatz-Hopkins Theorem, relating the homotopy fixed points of the Morava stabilizer group action on Lubin-Tate spectra to localized spheres, can be derived using algebraic geometry techniques involving monodromy on deformation stacks.

Contribution

It introduces a novel algebraic geometric approach to derive the Devinatz-Hopkins Theorem via monodromy on deformation stacks of formal groups.

Findings

Establishes a connection between formal spectral algebraic geometry and stable homotopy theory.

Provides a new geometric perspective on the action of the Morava stabilizer group.

Shows how to obtain the homotopy fixed point equivalence using algebraic geometry methods.

Abstract

In this note, we show how a continuous action of the Morava stabilizer group $\mathbb G_n$ on the Lubin-Tate spectrum $E_n$, satisfying the conclusion $E_n^{h\mathbb G_n}\simeq L_{K(n)} S$ of the Devinatz-Hopkins Theorem, may be obtained by monodromy on the stack of oriented deformations of formal groups in the context of formal spectral algebraic geometry.