arxiv: 1412.4041 · v2 · pith:TRNZIW5Knew · submitted 2014-12-12 · 🧮 math.KT · math.AT

On localization sequences in the algebraic K-theory of ring spectra

Benjamin Antieau , Tobias Barthel , David Gepner This is my paper

classification 🧮 math.KT math.AT

keywords fiberlocalizationringspectraalgebraalgebraicanswercomparing

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We identify the $K$-theoretic fiber of a localization of ring spectra in terms of the $K$-theory of the endomorphism algebra spectrum of a Koszul-type complex. Using this identification, we provide a negative answer to a question of Rognes for $n>1$ by comparing the traces of the fiber of the map $K(BP(n))\rightarrow K(E(n))$ and of $K(BP(n-1))$ in rational topological Hochschild homology.

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On localization sequences in the algebraic K-theory of ring spectra

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