Volume 21, issue 6 (2017)

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

Volume 22, 1 issue

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The chromatic splitting conjecture at $n=p=2$

Agnès Beaudry

Geometry & Topology 21 (2017) 3213–3230
Abstract

We show that the strongest form of Hopkins’ chromatic splitting conjecture, as stated by Hovey, cannot hold at chromatic level n = 2 at the prime p = 2. More precisely, for V (0), the mod 2 Moore spectrum, we prove that πkL1LK(2)V (0) is not zero when k is congruent to 3 modulo 8. We explain how this contradicts the decomposition of L1LK(2)S predicted by the chromatic splitting conjecture.

Keywords
K(2)-local, stable homotopy theory, Morava K-theory, chromatic assembly
Mathematical Subject Classification 2010
Primary: 55P60, 55Q45
References
Publication
Received: 3 April 2015
Revised: 7 December 2016
Accepted: 19 January 2017
Published: 31 August 2017
Proposed: Mark Behrens
Seconded: Stefan Schwede, Ralph Cohen
Authors
Agnès Beaudry
Department of Mathematics
University of Colorado
Boulder, CO
United States