Ravenel's May spectral sequence collapses immediately at large primes

Abstract

At large primes, the height $n$ Ravenel-May spectral sequence takes as input the cohomology of a certain solvable Lie ${\mathbb{F}}_p$-algebra, and produces as output the mod $p$ cohomology of the height $n$ strict Morava stabilizer group scheme. We construct simultaneous integral deformations of the height $n$ Morava stabilizer algebras and related objects, and we use them to prove that, for fixed $n$, the height $n$ Ravenel-May spectral sequence collapses for all sufficiently large primes $p$. Consequently, for large $p$, the mod $p$ cohomology of the strict Morava stabilizer group scheme is the cohomology of a finite-dimensional solvable Lie algebra, and is computable algorithmically.