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Creators/Authors contains: "Tamme, Georg"

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  1. ; ; ; (, Journal of the American Mathematical Society)
    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 depends on the T (n − 1) ⊕ T (n)-localization of R, again for n ≥ 1. As consequences, we deduce several vanishing results for telescopically localized K-theory, as well as an equivalence between K(R) and TC(τ≥0R) after T (n)-localization for n ≥ 2. 
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