Pro unitality and pro excision in algebraic K-theory and cyclic homology

M. Morrow
{"title":"Pro unitality and pro excision in algebraic K-theory and cyclic homology","authors":"M. Morrow","doi":"10.1515/CRELLE-2015-0007","DOIUrl":null,"url":null,"abstract":"We study pro excision in algebraic K-theory, following Suslin--Wodzicki, Cuntz--Quillen, Corti\\~nas, and Geisser--Hesselholt, as well as Artin--Rees and continuity properties of Andr\\'e--Quillen, Hochschild, and cyclic homology. Our key tool is to first establish the equivalence of various pro Tor vanishing conditions which appear in the literature. Using this we prove that all ideals of commutative, Noetherian rings are pro unital in a certain sense, and show that such ideals satisfy pro excision in $K$-theory as well as in cyclic and topological cyclic homology. In addition, our techniques yield a strong form of the pro Hochschild--Kostant--Rosenberg theorem, an extension to general base rings of the Cuntz--Quillen excision theorem in periodic cyclic homology, and a generalisation of the Fe\\u{\\i}gin--Tsygan theorem.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":"84 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/CRELLE-2015-0007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 29

Abstract

We study pro excision in algebraic K-theory, following Suslin--Wodzicki, Cuntz--Quillen, Corti\~nas, and Geisser--Hesselholt, as well as Artin--Rees and continuity properties of Andr\'e--Quillen, Hochschild, and cyclic homology. Our key tool is to first establish the equivalence of various pro Tor vanishing conditions which appear in the literature. Using this we prove that all ideals of commutative, Noetherian rings are pro unital in a certain sense, and show that such ideals satisfy pro excision in $K$-theory as well as in cyclic and topological cyclic homology. In addition, our techniques yield a strong form of the pro Hochschild--Kostant--Rosenberg theorem, an extension to general base rings of the Cuntz--Quillen excision theorem in periodic cyclic homology, and a generalisation of the Fe\u{\i}gin--Tsygan theorem.
代数k理论与循环同调中的亲酉性与亲切性
我们继Suslin- Wodzicki, Cuntz- Quillen, Corti - nas和Geisser- Hesselholt之后,研究了代数k理论中的亲切,以及Andr -Quillen, Hochschild和循环同调的Artin- Rees和连续性性质。我们的关键工具是首先建立文献中出现的各种pro - Tor消失条件的等价性。由此证明了交换noether环的所有理想在一定意义上都是亲酉的,并证明了这些理想在K -理论中满足亲切性,在环同调和拓扑环同调中满足亲切性。此外,我们的技术还得到了亲Hochschild—Kostant—Rosenberg定理的一个强形式,周期循环同调中Cuntz—Quillen切除定理对一般基环的推广,以及Fe\u{\i}gin—Tsygan定理的一个推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信