The action of the Morava stabilizer group on the coefficients of Morava E-theory at height 2

2025/03/06 by Andrew Salch, Salch, Andrew
Mathematics · #11S31 #14L05 #55P42 #55Q10 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.04686

openalex publication_date 2025/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate an explicit closed formula for the action of the height 2 full Morava stabilizer group on the coefficient ring of height 2 Morava E-theory. In particular, this yields an explicit, surprisingly simple closed formula for the action of the automorphism group of a height 2 formal group law on its Lubin-Tate deformation ring. The formula is of a combinatorial nature, given by sums over certain labelled ordered rooted trees.

Related

• A Computation of the Action of the Morava Stabilizer Group on the Lubin-Tate Deformation Ring
• Lubin-Tate theory, character theory, and power operations
• The Lubin-Tate stack and Gross-Hopkins duality
• Power operations for Morava E-theory of height 2 at the prime 2
• The cohomology of the height four Morava stabilizer group at large primes