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

{"title":"环谱代数k理论中的局部化序列","authors":"Benjamin Antieau, T. Barthel, David Gepner","doi":"10.4171/JEMS/771","DOIUrl":null,"url":null,"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.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"On localization sequences in the algebraic K-theory of ring spectra\",\"authors\":\"Benjamin Antieau, T. Barthel, David Gepner\",\"doi\":\"10.4171/JEMS/771\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/JEMS/771\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/JEMS/771","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv: K-Theory and Homology

自引率

0.00%

发文量