Geometry & Topology
- Geom. Topol.
- Volume 21, Number 6 (2017), 3213-3230.
The chromatic splitting conjecture at $n=p=2$
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Abstract
We show that the strongest form of Hopkins’ chromatic splitting conjecture, as stated by Hovey, cannot hold at chromatic level at the prime . More precisely, for , the mod Moore spectrum, we prove that is not zero when is congruent to modulo . We explain how this contradicts the decomposition of predicted by the chromatic splitting conjecture.
Article information
Source
Geom. Topol., Volume 21, Number 6 (2017), 3213-3230.
Dates
Received: 3 April 2015
Revised: 7 December 2016
Accepted: 19 January 2017
First available in Project Euclid: 16 November 2017
Permanent link to this document
https://projecteuclid.org/euclid.gt/1510859320
Digital Object Identifier
doi:10.2140/gt.2017.21.3213
Mathematical Reviews number (MathSciNet)
MR3692966
Zentralblatt MATH identifier
06779916
Subjects
Primary: 55P60: Localization and completion 55Q45: Stable homotopy of spheres
Keywords
K(2)-local stable homotopy theory Morava K-theory chromatic assembly
Citation
Beaudry, Agnès. The chromatic splitting conjecture at $n=p=2$. Geom. Topol. 21 (2017), no. 6, 3213--3230. doi:10.2140/gt.2017.21.3213. https://projecteuclid.org/euclid.gt/1510859320
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