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.