A remark on Hopkins' chromatic splitting conjecture

Abstract

Ravenel proved the remarkable fact that the $K$-theoretic localization $L_K{S}^0$ of the sphere spectrum has $\mathbb{Q}/\mathbb{Z}$ as homotopy group in dimension -2. Mike Hopkins' chromatic splitting conjecture implies more generally that there are $3^{n-1}$ copies of $(\mathbb{Q}/\mathbb{Z}{)}_p$ in the homotopy groups of the $E(n)$-localization of $S^0$; but where these copies occur can be confusing. We try here to simplify this book-keeping.

Small changes, notation perhaps improved

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