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arXiv · 2110.03733

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

Andrew J. Blumberg·Michael A. Mandell·Allen Yuan
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Abstract

We show that the map from $K({\mathbb S})$ 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 map $K({\mathbb S}_{(p)})_{(p)}\to \mathop{\rm holim} K(L^{f}_{n}{\mathbb S})_{(p)}$ is the inclusion of a wedge summand.

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BibTeXRIS

Andrew J. Blumberg, Michael A. Mandell, Allen Yuan. 2021-10-07. Chromatic convergence for the algebraic K-theory of the sphere spectrum. https://arxiv.org/abs/2110.03733

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