环谱代数k理论中的局部化序列

arXiv: K-Theory and Homology Pub Date : 2014-12-12 DOI:10.4171/JEMS/771

Benjamin Antieau, T. Barthel, David Gepner

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引用次数: 9

摘要

利用kozul型复合体的自同态代数谱的K理论，确定了环谱局域化的K理论光纤。通过比较映射$K(BP(n))\右行K(E(n))$和$K(BP(n-1))$在有理拓扑Hochschild同调中的纤维迹，我们给出了$n>1$的Rognes问题的否定答案。

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

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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arXiv: K-Theory and Homology

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