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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
The $\mathrm{Sp}_{k,n}$–local stable homotopy category

Drew Heard

Algebraic & Geometric Topology 23 (2023) 3655–3706
Abstract

We study the category of (K(k)K(k + 1)K(n))–local spectra, following a suggestion of Hovey and Strickland. When k = 0, this is equivalent to the category of E(n)–local spectra, while for k = n, this is the category of K(n)–local spectra, both of which have been studied in detail by Hovey and Strickland. Based on their ideas, we classify the localizing and colocalizing subcategories, and give characterizations of compact and dualizable objects. We construct an Adams-type spectral sequence and show that when p n it collapses with a horizontal vanishing line above filtration degree n2 + n k at the E2–page for the sphere spectrum. We then study the Picard group of (K(k)K(k + 1)K(n))–local spectra, showing that this group is algebraic, in a suitable sense, when p n. We also consider a version of Gross–Hopkins duality in this category. A key concept throughout is the use of descent.

Keywords
Morava $E$–theory, Morava $K$–theory, chromatic homotopy
Mathematical Subject Classification
Primary: 55P42, 55P60
Secondary: 55T15
References
Publication
Received: 13 August 2021
Revised: 15 February 2022
Accepted: 23 May 2022
Published: 5 November 2023
Authors
Drew Heard
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim
Norway

Open Access made possible by participating institutions via Subscribe to Open.