Volume 26, issue 1 (2022)

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

Volume 26
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Chromatic splitting for the $K(2)$–local sphere at $p=2$

Agnès Beaudry, Paul G Goerss and Hans-Werner Henn

Geometry & Topology 26 (2022) 377–476
DOI: 10.2140/gt.2022.26.377
Abstract

We calculate the homotopy type of L1LK(2)S0 and LK(1)LK(2)S0 at the prime 2, where LK(n) is localization with respect to Morava K–theory and L1 localization with respect to 2–local K–theory. In L1LK(2)S0 we find all the summands predicted by the Chromatic Splitting Conjecture, but we find some extra summands as well. An essential ingredient in our approach is the analysis of the continuous group cohomology H(𝔾2,E0), where 𝔾2 is the Morava stabilizer group and E0 = 𝕎[[u1]] is the ring of functions on the height 2 Lubin–Tate space. We show that the inclusion of the constants 𝕎 E0 induces an isomorphism on group cohomology, a radical simplification.

PDF Access Denied

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

We have not been able to recognize your IP address 44.192.65.228 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
chromatic splitting conjecture, chromatic homotopy theory, Morava K–theory localization of the sphere
Mathematical Subject Classification
Primary: 55P42, 55P60, 55Q51
References
Publication
Received: 8 October 2020
Revised: 18 February 2021
Accepted: 23 March 2021
Published: 5 April 2022
Proposed: Jesper Grodal
Seconded: Haynes R Miller, Stefan Schwede
Authors
Agnès Beaudry
Department of Mathematics
University of Colorado Boulder
Boulder, CO
United States
Paul G Goerss
Department of Mathematics
Northwestern University
Evanston, IL
United States
Hans-Werner Henn
Institut de Recherche Mathématique Avancée
CNRS
Université de Strasbourg
Strasbourg
France