Ravenel's May spectral sequence collapses immediately at large primes

2023/12/28 by Salch, A.
#17B56 #20J06 #55Q10 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.17185

Abstract

At large primes, the height n Ravenel-May spectral sequence takes as input the cohomology of a certain solvable Lie \mathbbF_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.

Related

• The mod p cohomology of the Morava stabilizer group at large primes
• The cohomology of the height four Morava stabilizer group at large primes
• The cohomology of S(n,k) relavent to Morava stablizer algebra
• A Mini-Course on Morava Stabilizer Groups and Their Cohomology
• Spectral moduli problems for level structures and an integral Jacquet-Langlands dual of Morava E-theory