English

A remark on Hopkins' chromatic splitting conjecture

Algebraic Topology 2015-03-31 v2

Abstract

Ravenel proved the remarkable fact that the KK-theoretic localization LKS0L_K S^0 of the sphere spectrum has Q/Z\mathbb{Q}/\mathbb{Z} as homotopy group in dimension -2. Mike Hopkins' chromatic splitting conjecture implies more generally that there are 3n13^{n-1} copies of (Q/Z)p(\mathbb{Q}/\mathbb{Z})_p in the homotopy groups of the E(n)E(n)-localization of S0S^0; but where these copies occur can be confusing. We try here to simplify this book-keeping.

Keywords

Cite

@article{arxiv.1406.3286,
  title  = {A remark on Hopkins' chromatic splitting conjecture},
  author = {Jack Morava},
  journal= {arXiv preprint arXiv:1406.3286},
  year   = {2015}
}

Comments

Small changes, notation perhaps improved

R2 v1 2026-06-22T04:37:18.541Z