The chromatic splitting conjecture at n = p = 2

Beaudry, Agnès¹

¹ Department of Mathematics, University of Colorado, Boulder, CO, United States

Geometry & topology, Tome 21 (2017) no. 6, pp. 3213-3230.

Résumé

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 $V\left(0\right)$, the mod $2$ Moore spectrum, we prove that ${\pi }_k{L}_1{L}_{K\left(2\right)}V\left(0\right)$ is not zero when $k$ is congruent to $-3$ modulo $8$. We explain how this contradicts the decomposition of $L_1{L}_{K\left(2\right)}S$ predicted by the chromatic splitting conjecture.

Détail

DOI : 10.2140/gt.2017.21.3213

Classification : 55P60, 55Q45
Keywords: K(2)-local, stable homotopy theory, Morava K-theory, chromatic assembly

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