Volume 20, issue 5 (2020)

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

Volume 20
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
An unstable change of rings for Morava $E$–theory

Robert Thompson

Algebraic & Geometric Topology 20 (2020) 2145–2176
Abstract

The Bousfield–Kan (or unstable Adams) spectral sequence can be constructed for various homology theories, such as Brown–Peterson homology theory BP, Johnson–Wilson theory E(n) or Morava E–theory En. For nice spaces the E2–term is given by Ext in a category of unstable comodules. We establish an unstable Morava change of rings isomorphism between Ext𝒰Γ B(B,M) and Ext𝒰E nEnIn(EnIn,EnBPM), where (B,ΓB) denotes the Hopf algebroid (vn1BPIn,vn1BPBPIn). We show that the latter groups can be interpreted as Ext in the category of continuous modules over the profinite monoid of endomorphisms of the Honda formal group law. By comparing this with the cohomology of the Morava stabilizer group we obtain an unstable Morava vanishing theorem when p 1 n

Keywords
unstable Adams spectral sequence, Morava changes of rings theorem
Mathematical Subject Classification 2010
Primary: 55N20, 55Q51, 55T15
References
Publication
Received: 20 September 2014
Revised: 24 August 2019
Accepted: 8 September 2019
Published: 4 November 2020
Authors
Robert Thompson
Department of Mathematics and Statistics
Hunter College and the Graduate Center, CUNY
New York, NY
United States