Volume 21, issue 5 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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 p(p) 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(4)–local E4–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 E4.

Keywords
formal groups, formal modules, stable homotopy, Morava stabilizer groups, stable homotopy groups
Mathematical Subject Classification 2010
Primary: 11S31, 14L05, 55N22, 55P42
References
Publication
Received: 14 July 2016
Revised: 31 August 2020
Accepted: 23 December 2020
Published: 31 October 2021
Authors
Andrew Salch
Department of Mathematics
Wayne State University
Detroit, MI
United States