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

Benjamin Antieau; Tobias Barthel; David Gepner

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

K-Theory and Homology 2017-07-17 v2 Algebraic Topology

Authors: Benjamin Antieau , Tobias Barthel , David Gepner

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.

Keywords

algebraic K-theory ring spectra localization sequences Koszul complex topological Hochschild homology BP(n) E(n)

Cite

@article{arxiv.1412.4041,
  title  = {On localization sequences in the algebraic K-theory of ring spectra},
  author = {Benjamin Antieau and Tobias Barthel and David Gepner},
  journal= {arXiv preprint arXiv:1412.4041},
  year   = {2017}
}

Comments

final version, to appear in the Journal of the European Mathematical Society

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

Abstract

Keywords

Cite

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