代数k理论与循环同调中的亲酉性与亲切性

M. Morrow
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引用次数: 29

摘要

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