| 书目名称 | The Local Structure of Algebraic K-Theory | | 编辑 | Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCart | | 视频video | | | 概述 | Covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen‘s topological cyclic homology, and gives a proof of the fact that the difference between the theories are ‘locally cons | | 丛书名称 | Algebra and Applications | | 图书封面 |  | | 描述 | Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen‘s calculations of finite fields and Suslin‘s calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen‘s topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen‘s calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen‘s calculations for local fields, and Voevodsky‘s calculations for the integers give insight into the diffeomorphisms of manifolds. | | 出版日期 | Book 2012 | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4471-4393-2 | | isbn_softcover | 978-1-4471-5904-9 | | isbn_ebook | 978-1-4471-4393-2Series ISSN 1572-5553 Series E-ISSN 2192-2950 | | issn_series | 1572-5553 | | copyright | Springer-Verlag London 2012 |
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发表于 2025-3-21 18:27:08
