#### Volume 21, issue 5 (2021)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Height four formal groups with quadratic complex multiplication

### Andrew Salch

Algebraic & Geometric Topology 21 (2021) 2141–2173
##### Abstract

We construct spectral sequences for computing the cohomology of automorphism groups of formal groups equipped with additional endomorphisms given by a $p$–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 ${ℚ}_{p}\left(\sqrt{p}\right)$ for primes $p>5$. 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 $8$ and total rank $80$. We then run the $K\left(4\right)$–local ${E}_{4}$–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 ${E}_{4}$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/agt

We have not been able to recognize your IP address 3.87.250.158 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.