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Localization for Thhku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories
Free Download Andrew J. Blumberg, "Localization for Thhku and the Topological Hochschild and Cyclic Homology of Waldhausen Categories "English | ISBN: 1470441780 | 2020 | 100 pages | PDF | 1019 KB
The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding $THH(ku)$, and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on $A(*)$.
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