Abstract

We prove a purity property in telescopically localized algebraic K-theory of ring spectra: For n≥1, the T(n)-localization of K(R) only depends on the T(0)⊕⋯⊕T(n)-localization of R. This complements a classical result of Waldhausen in rational K-theory. Combining our result with work of Clausen--Mathew--Naumann--Noel, one finds that LT(n)K(R) in fact only
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