We construct spectral sequences for computing the cohomology of automorphism
groups of formal groups equipped with additional endomorphisms given by a
–adic
number ring. We then compute the cohomology of the group of automorphisms
of a height four formal group law which commute with additional
endomorphisms of the group law by the ring of integers in the field
for
primes
.
This automorphism group is a large profinite subgroup of the height
four strict Morava stabilizer group. The group cohomology of this
group of automorphisms turns out to have cohomological dimension
and total rank
. We then run
the
–local
–Adams
spectral sequence to compute the homotopy groups of the homotopy fixed-point
spectrum of this group’s action on the Lubin–Tate/Morava spectrum
.
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