A Computation of the Action of the Morava Stabilizer Group on the Lubin-Tate Deformation Ring

TL;DR

This paper computes recursive approximations of the Morava stabilizer group's action on Lubin-Tate deformation rings, explicitly for height 3 and primes greater than 2, advancing understanding in chromatic homotopy theory.

Contribution

It introduces new recursive methods for approximating the stabilizer group's action at height h>2 and provides explicit calculations for height 3, extending prior work at height 2.

Findings

Recursive approximations for the stabilizer group's action

Explicit calculations for height 3 and p>2

Results align with known computations at height 2

Abstract

We compute recursive approximations of the action of the height $h \geq 2$ Morava stabilizer group on the associated Lubin-Tate deformation ring. We then specialize to the case $h=3$ and $p>2$ to calculate the action explicitly. These results are new for $h>2$ and agree with computations by Lader at height $h=2$.