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arXiv · 1412.4041

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

Benjamin Antieau·Tobias Barthel·David Gepner
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Abstract

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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Benjamin Antieau, Tobias Barthel, David Gepner. 2014-12-12. On localization sequences in the algebraic K-theory of ring spectra. https://arxiv.org/abs/1412.4041

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