Chromatic convergence for the algebraic K-theory of the sphere spectrum

Abstract

We show that the map from K(S) to its chromatic completion is a connective cover and identify the fiber in K-theoretic terms. We combine this with recent work of Land-Mathew-Meier-Tamme to prove a form of "Waldhausen's Chromatic Convergence Conjecture": we show that the mapis the inclusion of a wedge summand.