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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